Merge branch 'develop' into rheo

.github/CODEOWNERS

@@ -59,7 +59,8 @@ src/VTK/*             @rbberger
 
 # individual files in packages
 src/GPU/pair_vashishta_gpu.*        @andeplane
-src/KOKKOS/pair_vashishta_kokkos.*  @andeplane
+src/KOKKOS/pair_vashishta_kokkos.*  @andeplane @stanmoore1
+src/KOSSOS/pair_pod_kokkos.*        @exapde @stanmoore1
 src/MANYBODY/pair_vashishta_table.* @andeplane
 src/MANYBODY/pair_atm.*             @sergeylishchuk
 src/MANYBODY/pair_nb3b_screened.*   @flodesani

.gitignore

@@ -43,12 +43,12 @@ Thumbs.db
 
 #cmake
 /build*
-/CMakeCache.txt
+CMakeCache.txt
-/CMakeFiles/
+CMakeFiles
-/Testing
 /Makefile
-/Testing
+Testing
-/cmake_install.cmake
+Temporary
+cmake_install.cmake
 /lmp
 out/Debug
 out/RelWithDebInfo
@@ -60,3 +60,4 @@ src/Makefile.package.settings-e
 /cmake/build/x64-Debug-Clang
 /install/x64-GUI-MSVC
 /install
+.Rhistory

cmake/CMakeLists.txt

@@ -23,6 +23,7 @@ project(lammps CXX)
 set(SOVERSION 0)
 get_property(BUILD_IS_MULTI_CONFIG GLOBAL PROPERTY GENERATOR_IS_MULTI_CONFIG)
 
+include(GNUInstallDirs)
 get_filename_component(LAMMPS_DIR ${CMAKE_CURRENT_SOURCE_DIR}/.. ABSOLUTE)
 get_filename_component(LAMMPS_LIB_BINARY_DIR ${CMAKE_BINARY_DIR}/lib ABSOLUTE)
 # collect all executables and shared libs in the top level build folder
@@ -208,7 +209,7 @@ else()
   unset(CMAKE_CXX_CLANG_TIDY CACHE)
 endif()
 
-include(GNUInstallDirs)
+
 file(GLOB ALL_SOURCES CONFIGURE_DEPENDS ${LAMMPS_SOURCE_DIR}/[^.]*.cpp)
 file(GLOB MAIN_SOURCES CONFIGURE_DEPENDS ${LAMMPS_SOURCE_DIR}/main.cpp)
 list(REMOVE_ITEM ALL_SOURCES ${MAIN_SOURCES})
@@ -282,10 +283,10 @@ set(STANDARD_PACKAGES
   ML-HDNNP
   ML-IAP
   ML-PACE
+  ML-POD
   ML-QUIP
   ML-RANN
   ML-SNAP
-  ML-POD
   ML-UF3
   MOFFF
   MOLECULE

cmake/presets/all_off.cmake

@@ -26,8 +26,8 @@ set(ALL_PACKAGES
   DPD-REACT
   DPD-SMOOTH
   DRUDE
-  ELECTRODE
   EFF
+  ELECTRODE
   EXTRA-COMMAND
   EXTRA-COMPUTE
   EXTRA-DUMP

cmake/presets/all_on.cmake

@@ -28,8 +28,8 @@ set(ALL_PACKAGES
   DPD-REACT
   DPD-SMOOTH
   DRUDE
-  ELECTRODE
   EFF
+  ELECTRODE
   EXTRA-COMMAND
   EXTRA-COMPUTE
   EXTRA-DUMP

cmake/presets/mingw-cross.cmake

@@ -22,8 +22,8 @@ set(WIN_PACKAGES
   DPD-REACT
   DPD-SMOOTH
   DRUDE
-  ELECTRODE
   EFF
+  ELECTRODE
   EXTRA-COMMAND
   EXTRA-COMPUTE
   EXTRA-DUMP
@@ -33,7 +33,6 @@ set(WIN_PACKAGES
   FEP
   GPU
   GRANULAR
-  INTEL
   INTERLAYER
   KSPACE
   LEPTON

cmake/presets/windows.cmake

@@ -52,8 +52,8 @@ set(WIN_PACKAGES
   ORIENT
   PERI
   PHONON
-  POEMS
   PLUGIN
+  POEMS
   PTM
   QEQ
   QTB

doc/lammps.1

@@ -1,7 +1,7 @@
-.TH LAMMPS "1" "17 April 2024" "2024-04-17"
+.TH LAMMPS "1" "27 June 2024" "2024-06-27"
 .SH NAME
 .B LAMMPS
-\- Molecular Dynamics Simulator.  Version 17 April 2024
+\- Molecular Dynamics Simulator.  Version 27 June 2024
 
 .SH SYNOPSIS
 .B lmp

doc/src/Commands_compute.rst

@@ -108,6 +108,10 @@ KOKKOS, o = OPENMP, t = OPT.
    * :doc:`pe/mol/tally <compute_tally>`
    * :doc:`pe/tally <compute_tally>`
    * :doc:`plasticity/atom <compute_plasticity_atom>`
+   * :doc:`pod/atom <compute_pod_atom>`
+   * :doc:`podd/atom <compute_pod_atom>`
+   * :doc:`pod/local <compute_pod_atom>`
+   * :doc:`pod/global <compute_pod_atom>`
    * :doc:`pressure <compute_pressure>`
    * :doc:`pressure/alchemy <compute_pressure_alchemy>`
    * :doc:`pressure/uef <compute_pressure_uef>`

doc/src/Commands_pair.rst

@@ -247,7 +247,7 @@ OPT.
    * :doc:`pace (k) <pair_pace>`
    * :doc:`pace/extrapolation (k) <pair_pace>`
    * :doc:`pedone (o) <pair_pedone>`
-   * :doc:`pod <pair_pod>`
+   * :doc:`pod (k) <pair_pod>`
    * :doc:`peri/eps <pair_peri>`
    * :doc:`peri/lps (o) <pair_peri>`
    * :doc:`peri/pmb (o) <pair_peri>`

doc/src/Commands_removed.rst

@@ -151,10 +151,10 @@ and allow running LAMMPS with GPU acceleration.
 i-PI tool
 ---------
 
-.. versionchanged:: TBD
+.. versionchanged:: 27June2024
 
 The i-PI tool has been removed from the LAMMPS distribution.  Instead,
-instructions to install i-PI from PyPi via pip are provided.
+instructions to install i-PI from PyPI via pip are provided.
 
 restart2data tool
 -----------------

doc/src/Developer_utils.rst

@@ -211,6 +211,9 @@ Argument processing
 .. doxygenfunction:: bounds
    :project: progguide
 
+.. doxygenfunction:: bounds_typelabel
+   :project: progguide
+
 .. doxygenfunction:: expand_args
    :project: progguide
 

doc/src/Developer_write_pair.rst

@@ -50,6 +50,30 @@ We are looking at the following cases:
 - `Case 3: a potential requiring communication`_
 - `Case 4: potentials without a compute() function`_
 
+Package and build system considerations
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+In general, new pair styles should be added to the :ref:`EXTRA-PAIR
+package <PKG-EXTRA-PAIR>` unless they are an accelerated pair style and
+then they should be added to the corresponding accelerator package
+(:ref:`GPU <PKG-GPU>`, :ref:`INTEL <PKG-INTEL>`, :ref:`KOKKOS
+<PKG-KOKKOS>`, :ref:`OPENMP <PKG-OPENMP>`, :ref:`OPT <PKG-OPT>`).  If
+you feel that your contribution should be added to a different package,
+please consult with the LAMMPS developers first.
+
+The contributed code needs to support the :doc:`traditional GNU make
+build process <Build_make>` **and** the :doc:`CMake build process
+<Build_cmake>`.  For the GNU make process and if the package has an
+``Install.sh`` file, most likely that file needs to be updated to
+correctly copy the sources when installing the package and properly
+delete them when uninstalling.  This is particularly important when
+added a new pair style that is a derived class from an existing pair
+style in a package, so that its installation depends on the the
+installation status of the package of the derived class.  For the CMake
+process, it is sometimes necessary to make changes to the package
+specific CMake scripting in ``cmake/Modules/Packages``.
+
+
 ----
 
 Case 1: a pairwise additive model

doc/src/Howto_bioFF.rst

@@ -1,6 +1,10 @@
 CHARMM, AMBER, COMPASS, and DREIDING force fields
 =================================================
 
+A compact summary of the concepts, definitions, and properties of
+force fields with explicit bonded interactions (like the ones discussed
+in this HowTo) is given in :ref:`(Gissinger) <Typelabel2>`.
+
 A force field has 2 parts: the formulas that define it and the
 coefficients used for a particular system.  Here we only discuss
 formulas implemented in LAMMPS that correspond to formulas commonly used
@@ -11,12 +15,42 @@ commands like :doc:`pair_coeff <pair_coeff>` or :doc:`bond_coeff
 <bond_coeff>` and so on.  See the :doc:`Tools <Tools>` doc page for
 additional tools that can use CHARMM, AMBER, or Materials Studio
 generated files to assign force field coefficients and convert their
-output into LAMMPS input.
+output into LAMMPS input. LAMMPS input scripts can also be generated by
+`charmm-gui.org <https://charmm-gui.org/>`_.
 
-See :ref:`(MacKerell) <howto-MacKerell>` for a description of the CHARMM
+CHARMM and AMBER
-force field.  See :ref:`(Cornell) <howto-Cornell>` for a description of
+----------------
-the AMBER force field.  See :ref:`(Sun) <howto-Sun>` for a description
+
-of the COMPASS force field.
+The `CHARMM force field
+<https://mackerell.umaryland.edu/charmm_ff.shtml>`_ :ref:`(MacKerell)
+<howto-MacKerell>` and `AMBER force field
+<https://ambermd.org/AmberModels.php>`_ :ref:`(Cornell) <howto-Cornell>`
+have potential energy function of the form
+
+.. math::
+
+  V & = \sum_{bonds} E_b + \sum_{angles} \!E_a + \!\overbrace{\sum_{dihedral} \!\!E_d}^{\substack{
+         \text{charmm} \\
+        \text{charmmfsw}
+      }} +\!\!\! \sum_{impropers} \!\!\!E_i \\[.6em]
+      & \quad + \!\!\!\!\!\!\!\!\!\!\underbrace{~\sum_{pairs} \left(E_{LJ}+E_{coul}\right)}_{\substack{
+         \text{lj/charmm/coul/charmm} \\
+        \text{lj/charmm/coul/charmm/implicit} \\
+        \text{lj/charmm/coul/long} \\
+        \text{lj/charmm/coul/msm} \\
+         \text{lj/charmmfsw/coul/charmmfsh} \\
+        \text{lj/charmmfsw/coul/long}
+      }} \!\!\!\!\!\!\!\!+ \!\!\sum_{special}\! E_s + \!\!\!\!\sum_{residues} \!\!\!{\scriptstyle\mathrm{CMAP}(\phi,\psi)}
+
+
+The terms are computed by bond styles (relationship between 2 atoms),
+angle styles (between 3 atoms) , dihedral/improper styles (between 4
+atoms), pair styles (non-covalently bonded pair interactions) and
+special bonds. The CMAP term (see :doc:`fix cmap <fix_cmap>` command for
+details) corrects for pairs of dihedral angles ("Correction MAP") to
+significantly improve the structural and dynamic properties of proteins
+in crystalline and solution environments :ref:`(Brooks)
+<howto-Brooks>`. The AMBER force field does not include the CMAP term.
 
 The interaction styles listed below compute force field formulas that
 are consistent with common options in CHARMM or AMBER.  See each
@@ -31,10 +65,81 @@ command's documentation for the formula it computes.
 * :doc:`pair_style <pair_charmm>` lj/charmm/coul/charmm
 * :doc:`pair_style <pair_charmm>` lj/charmm/coul/charmm/implicit
 * :doc:`pair_style <pair_charmm>` lj/charmm/coul/long
-
 * :doc:`special_bonds <special_bonds>` charmm
 * :doc:`special_bonds <special_bonds>` amber
 
+The pair styles compute Lennard Jones (LJ) and Coulombic interactions
+with additional switching or shifting functions that ramp the energy
+and/or force smoothly to zero between an inner :math:`(a)` and outer
+:math:`(b)` cutoff. The older styles with *charmm* (not *charmmfsw* or
+*charmmfsh*\ ) in their name compute the LJ and Coulombic interactions
+with an energy switching function (esw) S(r) which ramps the energy
+smoothly to zero between the inner and outer cutoff. This can cause
+irregularities in pairwise forces (due to the discontinuous second
+derivative of energy at the boundaries of the switching region), which
+in some cases can result in complications in energy minimization and
+detectable artifacts in MD simulations.
+
+.. grid:: 1 1 2 2
+
+   .. grid-item::
+
+      .. math::
+
+         LJ(r) &= 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} -
+                  \left(\frac{\sigma}{r}\right)^6 \right]\\[.6em]
+         C(r) &= \frac{C q_i q_j}{ \epsilon r}\\[.6em]
+         S(r) &=  \frac{ \left(b^2 - r^2\right)^2 \left(b^2 + 2r^2 - 3{a^2}\right)}
+                 { \left(b^2 - a^2\right)^3 }\\[.6em]
+         E_{LJ}(r) &=  \begin{cases}
+           LJ(r), & r \leq a \\
+           LJ(r) S(r), & a < r \leq b \\
+           0, &r > b
+         \end{cases} \\[.6em]
+         E_{coul}(r) &=  \begin{cases}
+           C(r), & r \leq a \\
+           C(r) S(r), & a < r \leq b \\
+           0, & r > b
+         \end{cases}
+
+   .. grid-item::
+
+      .. image:: img/howto_charmm_ELJ.png
+         :align: center
+
+The newer styles with *charmmfsw* or *charmmfsh* in their name replace
+energy switching with force switching (fsw) for LJ interactions and
+force shifting (fsh) functions for Coulombic interactions
+:ref:`(Steinbach) <howto-Steinbach>`
+
+.. grid:: 1 1 2 2
+
+   .. grid-item::
+
+      .. math::
+
+           E_{LJ}(r) = & \begin{cases}
+       4  \epsilon \sigma^6  \left(\frac{\displaystyle\sigma
+         ^6-r^6}{\displaystyle r^{12}}-\frac{\displaystyle\sigma ^6}{\displaystyle a^6
+         b^6}+\frac{\displaystyle 1}{\displaystyle a^3 b^3}\right) & r\leq a \\
+       \frac{\displaystyle 4 \epsilon \sigma^6   \left(\sigma ^6
+         \left(b^6-r^6\right)^2-b^3 r^6 \left(a^3+b^3\right)
+         \left(b^3-r^3\right)^2\right)}{\displaystyle b^6 r^{12}
+         \left(b^6-a^6\right)} & a<r \leq b\\
+         0, & r>b
+        \end{cases}\\[.6em]
+         E_{coul}(r) & =  \begin{cases}
+              C(r) \frac{\displaystyle (b-r)^2}{\displaystyle r b^2}, &  r \leq b \\
+              0, & r > b
+            \end{cases}
+
+   .. grid-item::
+      .. image:: img/howto_charmmfsw_ELJ.png
+         :align: center
+
+These styles are used by LAMMPS input scripts generated by
+https://charmm-gui.org/ :ref:`(Brooks) <howto-Brooks>`.
+
 .. note::
 
    For CHARMM, newer *charmmfsw* or *charmmfsh* styles were released in
@@ -43,17 +148,33 @@ command's documentation for the formula it computes.
    <pair_charmm>` and :doc:`dihedral charmm <dihedral_charmm>` doc
    pages.
 
+.. note::
+
+  The TIP3P water model is strongly recommended for use with the CHARMM
+  force field. In fact, `"using the SPC model with CHARMM parameters is
+  a bad idea"
+  <https://matsci.org/t/using-spc-water-with-charmm-ff/24715>`_ and `"to
+  enable TIP4P style water in CHARMM, you would have to write a new pair
+  style"
+  <https://matsci.org/t/hybrid-pair-styles-for-charmm-and-tip4p-ew/32609>`_
+  . LAMMPS input scripts generated by Solution Builder on https://charmm-gui.org
+  use TIP3P molecules for solvation.  Any other water model can and
+  probably will lead to false conclusions.
+
+COMPASS
+-------
+
 COMPASS is a general force field for atomistic simulation of common
 organic molecules, inorganic small molecules, and polymers which was
-developed using ab initio and empirical parameterization techniques.
+developed using ab initio and empirical parameterization techniques
-See the :doc:`Tools <Tools>` page for the msi2lmp tool for creating
+:ref:`(Sun) <howto-Sun>`.  See the :doc:`Tools <Tools>` page for the
-LAMMPS template input and data files from BIOVIA's Materials Studio
+msi2lmp tool for creating LAMMPS template input and data files from
-files.  Please note that the msi2lmp tool is very old and largely
+BIOVIA's Materials Studio files.  Please note that the msi2lmp tool is
-unmaintained, so it does not support all features of Materials Studio
+very old and largely unmaintained, so it does not support all features
-provided force field files, especially additions during the last decade.
+of Materials Studio provided force field files, especially additions
-You should watch the output carefully and compare results, where
+during the last decade.  You should watch the output carefully and
-possible.  See :ref:`(Sun) <howto-Sun>` for a description of the COMPASS force
+compare results, where possible.  See :ref:`(Sun) <howto-Sun>` for a
-field.
+description of the COMPASS force field.
 
 These interaction styles listed below compute force field formulas that
 are consistent with the COMPASS force field.  See each command's
@@ -70,14 +191,21 @@ documentation for the formula it computes.
 
 * :doc:`special_bonds <special_bonds>` lj/coul 0 0 1
 
-DREIDING is a generic force field developed by the `Goddard group <http://www.wag.caltech.edu>`_ at Caltech and is useful for
+DREIDING
-predicting structures and dynamics of organic, biological and main-group
+--------
-inorganic molecules. The philosophy in DREIDING is to use general force
+
-constants and geometry parameters based on simple hybridization
+DREIDING is a generic force field developed by the `Goddard group
-considerations, rather than individual force constants and geometric
+<http://www.wag.caltech.edu>`_ at Caltech and is useful for predicting
-parameters that depend on the particular combinations of atoms involved
+structures and dynamics of organic, biological and main-group inorganic
-in the bond, angle, or torsion terms. DREIDING has an :doc:`explicit hydrogen bond term <pair_hbond_dreiding>` to describe interactions involving a
+molecules.  The philosophy in DREIDING is to use general force constants
-hydrogen atom on very electronegative atoms (N, O, F).
+and geometry parameters based on simple hybridization considerations,
+rather than individual force constants and geometric parameters that
+depend on the particular combinations of atoms involved in the bond,
+angle, or torsion terms.  DREIDING has an :doc:`explicit hydrogen bond
+term <pair_hbond_dreiding>` to describe interactions involving a
+hydrogen atom on very electronegative atoms (N, O, F).  Unlike CHARMM
+or AMBER, the DREIDING force field has not been parameterized for
+considering solvents (like water).
 
 See :ref:`(Mayo) <howto-Mayo>` for a description of the DREIDING force field
 
@@ -110,21 +238,31 @@ documentation for the formula it computes.
 
 ----------
 
+.. _Typelabel2:
+
+**(Gissinger)** J. R. Gissinger, I. Nikiforov, Y. Afshar, B. Waters, M. Choi, D. S. Karls, A. Stukowski, W. Im, H. Heinz, A. Kohlmeyer, and E. B. Tadmor, J Phys Chem B, 128, 3282-3297 (2024).
+
 .. _howto-MacKerell:
 
-**(MacKerell)** MacKerell, Bashford, Bellott, Dunbrack, Evanseck, Field,
+**(MacKerell)** MacKerell, Bashford, Bellott, Dunbrack, Evanseck, Field, Fischer, Gao, Guo, Ha, et al (1998).  J Phys Chem, 102, 3586 . https://doi.org/10.1021/jp973084f
-Fischer, Gao, Guo, Ha, et al, J Phys Chem, 102, 3586 (1998).
 
 .. _howto-Cornell:
 
-**(Cornell)** Cornell, Cieplak, Bayly, Gould, Merz, Ferguson,
+**(Cornell)** Cornell, Cieplak, Bayly, Gould, Merz, Ferguson, Spellmeyer, Fox, Caldwell, Kollman (1995).  JACS 117, 5179-5197. https://doi.org/10.1021/ja00124a002
-Spellmeyer, Fox, Caldwell, Kollman, JACS 117, 5179-5197 (1995).
+
+.. _howto-Steinbach:
+
+**(Steinbach)** Steinbach, Brooks (1994). J Comput Chem, 15, 667. https://doi.org/10.1002/jcc.540150702
+
+.. _howto-Brooks:
+
+**(Brooks)** Brooks, et al (2009). J Comput Chem, 30, 1545. https://onlinelibrary.wiley.com/doi/10.1002/jcc.21287
 
 .. _howto-Sun:
 
-**(Sun)** Sun, J. Phys. Chem. B, 102, 7338-7364 (1998).
+**(Sun)** Sun (1998). J. Phys. Chem. B, 102, 7338-7364. https://doi.org/10.1021/jp980939v
 
 .. _howto-Mayo:
 
-**(Mayo)** Mayo, Olfason, Goddard III, J Phys Chem, 94, 8897-8909
+**(Mayo)** Mayo, Olfason, Goddard III (1990). J Phys Chem, 94, 8897-8909. https://doi.org/10.1021/j100389a010
-(1990).
+

doc/src/Tools.rst

@@ -379,7 +379,7 @@ See README file in the tools/fep directory.
 i-PI tool
 -------------------
 
-.. versionchanged:: TBD
+.. versionchanged:: 27June2024
 
 The tools/i-pi directory used to contain a bundled version of the i-PI
 software package for use with LAMMPS.  This version, however, was
@@ -389,7 +389,7 @@ The i-PI package was created and is maintained by Michele Ceriotti,
 michele.ceriotti at gmail.com, to interface to a variety of molecular
 dynamics codes.
 
-i-PI is now available via PyPi using the pip package manager at:
+i-PI is now available via PyPI using the pip package manager at:
 https://pypi.org/project/ipi/
 
 Here are the commands to set up a virtual environment and install
@@ -839,7 +839,7 @@ and LAMMPS GUI can be launched from anywhere from the command line.
 
 The standard CMake build procedure can be applied and the
 ``mingw-cross.cmake`` preset used. By using ``mingw64-cmake`` the CMake
-command will automatically include a suitable CMake toolset file (the
+command will automatically include a suitable CMake toolchain file (the
 regular cmake command can be used after that to modify the configuration
 settings, if needed).  After building the libraries and executables,
 you can build the target 'zip' (i.e. ``cmake --build <build dir> --target zip``

doc/src/atom_modify.rst

@@ -71,11 +71,11 @@ all atoms, e.g. in a data or restart file.
    atom IDs are required, due to how neighbor lists are built.
 
 The *map* keyword determines how atoms with specific IDs are found
-when required.  An example are the bond (angle, etc) methods which
+when required.  For example, the bond (angle, etc) methods need to
-need to find the local index of an atom with a specific global ID
+find the local index of an atom with a specific global ID which is a
-which is a bond (angle, etc) partner.  LAMMPS performs this operation
+bond (angle, etc) partner.  LAMMPS performs this operation efficiently
-efficiently by creating a "map", which is either an *array* or *hash*
+by creating a "map", which is either an *array* or *hash* table, as
-table, as described below.
+described below.
 
 When the *map* keyword is not specified in your input script, LAMMPS
 only creates a map for :doc:`atom_styles <atom_style>` for molecular
@@ -83,34 +83,39 @@ systems which have permanent bonds (angles, etc).  No map is created
 for atomic systems, since it is normally not needed.  However some
 LAMMPS commands require a map, even for atomic systems, and will
 generate an error if one does not exist.  The *map* keyword thus
-allows you to force the creation of a map.  The *yes* value will
+allows you to force the creation of a map.
-create either an *array* or *hash* style map, as explained in the next
-paragraph.  The *array* and *hash* values create an array-style or
-hash-style map respectively.
 
-For an *array*\ -style map, each processor stores a lookup table of
+Specifying a value of *yes* will create either an array-style or
-length N, where N is the largest atom ID in the system.  This is a
+hash-style map, depending on the size of the system.  If no atom ID is
-fast, simple method for many simulations, but requires too much memory
+larger than 1 million, then an array-style map is used, otherwise a
-for large simulations.  For a *hash*\ -style map, a hash table is
+hash-style map is used.  Specifying a value of *array* or *hash*
-created on each processor, which finds an atom ID in constant time
+creates an array-style or hash-style map respectively, regardless of
-(independent of the global number of atom IDs).  It can be slightly
+the size of the system.
-slower than the *array* map, but its memory cost is proportional to
-the number of atoms owned by a processor, i.e. N/P when N is the total
-number of atoms in the system and P is the number of processors.
 
-The *first* keyword allows a :doc:`group <group>` to be specified whose
+For an array-style map, each processor stores a lookup table of length
-atoms will be maintained as the first atoms in each processor's list
+N, where N is the largest atom ID in the system.  This is a fast,
-of owned atoms.  This in only useful when the specified group is a
+simple method for many simulations, but requires too much memory for
-small fraction of all the atoms, and there are other operations LAMMPS
+large simulations.  For a hash-style map, a hash table is created on
-is performing that will be sped-up significantly by being able to loop
+each processor, which finds an atom ID in constant time (independent
-over the smaller set of atoms.  Otherwise the reordering required by
+of the global number of atom IDs).  It can be slightly slower than the
-this option will be a net slow-down.  The :doc:`neigh_modify include <neigh_modify>` and :doc:`comm_modify group <comm_modify>`
+*array* map, but its memory cost is proportional to the number of
-commands are two examples of commands that require this setting to
+atoms owned by a processor, i.e. N/P when N is the total number of
-work efficiently.  Several :doc:`fixes <fix>`, most notably time
+atoms in the system and P is the number of processors.
-integration fixes like :doc:`fix nve <fix_nve>`, also take advantage of
+
-this setting if the group they operate on is the group specified by
+The *first* keyword allows a :doc:`group <group>` to be specified
-this command.  Note that specifying "all" as the group-ID effectively
+whose atoms will be maintained as the first atoms in each processor's
-turns off the *first* option.
+list of owned atoms.  This in only useful when the specified group is
+a small fraction of all the atoms, and there are other operations
+LAMMPS is performing that will be sped-up significantly by being able
+to loop over the smaller set of atoms.  Otherwise the reordering
+required by this option will be a net slow-down.  The
+:doc:`neigh_modify include <neigh_modify>` and :doc:`comm_modify group
+<comm_modify>` commands are two examples of commands that require this
+setting to work efficiently.  Several :doc:`fixes <fix>`, most notably
+time integration fixes like :doc:`fix nve <fix_nve>`, also take
+advantage of this setting if the group they operate on is the group
+specified by this command.  Note that specifying "all" as the group-ID
+effectively turns off the *first* option.
 
 It is OK to use the *first* keyword with a group that has not yet been
 defined, e.g. to use the atom_modify first command at the beginning of
@@ -148,15 +153,16 @@ cache locality will be undermined.
 
 .. note::
 
-   Running a simulation with sorting on versus off should not
+   Running a simulation with sorting on versus off should not change
-   change the simulation results in a statistical sense.  However, a
+   the simulation results in a statistical sense.  However, a
-   different ordering will induce round-off differences, which will lead
+   different ordering will induce round-off differences, which will
-   to diverging trajectories over time when comparing two simulations.
+   lead to diverging trajectories over time when comparing two
-   Various commands, particularly those which use random numbers
+   simulations.  Various commands, particularly those which use random
-   (e.g. :doc:`velocity create <velocity>`, and :doc:`fix langevin <fix_langevin>`), may generate (statistically identical)
+   numbers (e.g. :doc:`velocity create <velocity>`, and :doc:`fix
-   results which depend on the order in which atoms are processed.  The
+   langevin <fix_langevin>`), may generate (statistically identical)
-   order of atoms in a :doc:`dump <dump>` file will also typically change
+   results which depend on the order in which atoms are processed.
-   if sorting is enabled.
+   The order of atoms in a :doc:`dump <dump>` file will also typically
+   change if sorting is enabled.
 
 .. note::
 
@@ -183,12 +189,13 @@ Default
 
 By default, *id* is yes.  By default, atomic systems (no bond topology
 info) do not use a map.  For molecular systems (with bond topology
-info), a map is used.  The default map style is array if no atom ID is
+info), the default is to use a map of either *array* or *hash* style
-larger than 1 million, otherwise the default is hash.  By default, a
+depending on the size of the sustem, as explained above for the *map
-"first" group is not defined.  By default, sorting is enabled with a
+yes* keyword/value option.  By default, a *first* group is not
-frequency of 1000 and a binsize of 0.0, which means the neighbor
+defined.  By default, sorting is enabled with a frequency of 1000 and
-cutoff will be used to set the bin size. If no neighbor cutoff is
+a binsize of 0.0, which means the neighbor cutoff will be used to set
-defined, sorting will be turned off.
+the bin size. If no neighbor cutoff is defined, sorting will be turned
+off.
 
 ----------
 

doc/src/compute.rst

@@ -272,6 +272,10 @@ The individual style names on the :doc:`Commands compute <Commands_compute>` pag
 * :doc:`pe/mol/tally <compute_tally>` - potential energy between two groups of atoms separated into intermolecular and intramolecular components via the tally callback mechanism
 * :doc:`pe/tally <compute_tally>` - potential energy between two groups of atoms via the tally callback mechanism
 * :doc:`plasticity/atom <compute_plasticity_atom>` - Peridynamic plasticity for each atom
+* :doc:`pod/atom <compute_pod_atom>` - POD descriptors for each atom
+* :doc:`podd/atom <compute_pod_atom>` - derivative of POD descriptors for each atom
+* :doc:`pod/local <compute_pod_atom>` - local POD descriptors and their derivatives
+* :doc:`pod/global <compute_pod_atom>` - global POD descriptors and their derivatives
 * :doc:`pressure <compute_pressure>` - total pressure and pressure tensor
 * :doc:`pressure/alchemy <compute_pressure_alchemy>` - mixed system total pressure and pressure tensor for :doc:`fix alchemy <fix_alchemy>` runs
 * :doc:`pressure/uef <compute_pressure_uef>` - pressure tensor in the reference frame of an applied flow field

doc/src/compute_pod_atom.rst

@@ -0,0 +1,145 @@
+.. index:: compute pod/atom
+.. index:: compute podd/atom
+.. index:: compute pod/local
+.. index:: compute pod/global
+
+compute pod/atom command
+========================
+
+compute podd/atom command
+=========================
+
+compute pod/local command
+=========================
+
+compute pod/global command
+==========================
+
+Syntax
+""""""
+
+.. code-block:: LAMMPS
+
+   compute ID group-ID pod/atom param.pod coefficients.pod
+   compute ID group-ID podd/atom param.pod coefficients.pod
+   compute ID group-ID pod/local param.pod coefficients.pod
+   compute ID group-ID pod/global param.pod coefficients.pod
+
+* ID, group-ID are documented in :doc:`compute <compute>` command
+* pod/atom = style name of this compute command
+* param.pod = the parameter file specifies parameters of the POD descriptors
+* coefficients.pod = the coefficient file specifies coefficients of the POD potential
+
+Examples
+""""""""
+
+.. code-block:: LAMMPS
+
+   compute d all pod/atom Ta_param.pod
+   compute dd all podd/atom Ta_param.pod
+   compute ldd all pod/local Ta_param.pod
+   compute gdd all podd/global Ta_param.pod
+   compute d all pod/atom Ta_param.pod Ta_coefficients.pod
+   compute dd all podd/atom Ta_param.pod Ta_coefficients.pod
+   compute ldd all pod/local Ta_param.pod Ta_coefficients.pod
+   compute gdd all podd/global Ta_param.pod Ta_coefficients.pod
+
+Description
+"""""""""""
+
+.. versionadded:: 27June2024
+
+Define a computation that calculates a set of quantities related to the
+POD descriptors of the atoms in a group. These computes are used
+primarily for calculating the dependence of energy and force components
+on the linear coefficients in the :doc:`pod pair_style <pair_pod>`,
+which is useful when training a POD potential to match target data. POD
+descriptors of an atom are characterized by the radial and angular
+distribution of neighbor atoms. The detailed mathematical definition is
+given in the papers by :ref:`(Nguyen and Rohskopf) <Nguyen20222c>`,
+:ref:`(Nguyen2023) <Nguyen20232c>`, :ref:`(Nguyen2024) <Nguyen20242c>`,
+and :ref:`(Nguyen and Sema) <Nguyen20243c>`.
+
+Compute *pod/atom* calculates the per-atom POD descriptors.
+
+Compute *podd/atom* calculates derivatives of the per-atom POD
+descriptors with respect to atom positions.
+
+Compute *pod/local* calculates the per-atom POD descriptors and their
+derivatives with respect to atom positions.
+
+Compute *pod/global* calculates the global POD descriptors and their
+derivatives with respect to atom positions.
+
+Examples how to use Compute POD commands are found in the directory
+``examples/PACKAGES/pod``.
+
+
+.. warning::
+
+   All of these compute styles produce *very* large per-atom output
+   arrays that scale with the total number of atoms in the system.
+   This will result in *very* large memory consumption for systems
+   with a large number of atoms.
+
+----------
+
+Output info
+"""""""""""
+
+Compute *pod/atom* produces an 2D array of size :math:`N \times M`,
+where :math:`N` is the number of atoms and :math:`M` is the number of
+descriptors. Each column corresponds to a particular POD descriptor.
+
+Compute *podd/atom* produces an 2D array of size :math:`N \times (M * 3
+N)`. Each column corresponds to a particular derivative of a POD
+descriptor.
+
+Compute *pod/local* produces an 2D array of size :math:`(1 + 3N) \times
+(M * N)`.  The first row contains the per-atom descriptors, and the last
+3N rows contain the derivatives of the per-atom descriptors with respect
+to atom positions.
+
+Compute *pod/global* produces an 2D array of size :math:`(1 + 3N) \times
+(M)`.  The first row contains the global descriptors, and the last 3N
+rows contain the derivatives of the global descriptors with respect to
+atom positions.
+
+Restrictions
+""""""""""""
+
+These computes are part of the ML-POD package.  They are only enabled
+if LAMMPS was built with that package.  See the :doc:`Build package
+<Build_package>` page for more info.
+
+Related commands
+""""""""""""""""
+
+:doc:`fitpod <fitpod_command>`,
+:doc:`pair_style pod <pair_pod>`
+
+
+Default
+"""""""
+
+none
+
+----------
+
+.. _Nguyen20222c:
+
+**(Nguyen and Rohskopf)** Nguyen and Rohskopf,  Journal of Computational Physics, 480, 112030, (2023).
+
+.. _Nguyen20232c:
+
+**(Nguyen2023)** Nguyen, Physical Review B, 107(14), 144103, (2023).
+
+.. _Nguyen20242c:
+
+**(Nguyen2024)** Nguyen, Journal of Computational Physics, 113102, (2024).
+
+.. _Nguyen20243c:
+
+**(Nguyen and Sema)** Nguyen and Sema, https://arxiv.org/abs/2405.00306, (2024).
+
+

doc/src/fitpod_command.rst

@@ -1,18 +1,19 @@
 .. index:: fitpod
 
 fitpod command
-======================
+==============
 
 Syntax
 """"""
 
 .. code-block:: LAMMPS
 
-   fitpod Ta_param.pod Ta_data.pod
+   fitpod Ta_param.pod Ta_data.pod Ta_coefficients.pod
 
 * fitpod = style name of this command
 * Ta_param.pod = an input file that describes proper orthogonal descriptors (PODs)
 * Ta_data.pod = an input file that specifies DFT data used to fit a POD potential
+* Ta_coefficients.pod (optional) = an input file that specifies trainable coefficients of a POD potential
 
 Examples
 """"""""
@@ -20,20 +21,26 @@ Examples
 .. code-block:: LAMMPS
 
    fitpod Ta_param.pod Ta_data.pod
+   fitpod Ta_param.pod Ta_data.pod Ta_coefficients.pod
 
 Description
 """""""""""
 .. versionadded:: 22Dec2022
 
 Fit a machine-learning interatomic potential (ML-IAP) based on proper
-orthogonal descriptors (POD).  Two input files are required for this
+orthogonal descriptors (POD); please see :ref:`(Nguyen and Rohskopf)
-command. The first input file describes a POD potential parameter
+<Nguyen20222a>`, :ref:`(Nguyen2023) <Nguyen20232a>`, :ref:`(Nguyen2024)
-settings, while the second input file specifies the DFT data used for
+<Nguyen20242a>`, and :ref:`(Nguyen and Sema) <Nguyen20243a>` for details.
-the fitting procedure.
+The fitted POD potential can be used to run MD simulations via
+:doc:`pair_style pod <pair_pod>`.
 
-The table below has one-line descriptions of all the keywords that can
+Two input files are required for this command. The first input file
-be used in the first input file (i.e. ``Ta_param.pod`` in the example
+describes a POD potential parameter settings, while the second input
-above):
+file specifies the DFT data used for the fitting procedure. All keywords
+except *species* have default values. If a keyword is not set in the
+input file, its default value is used. The table below has one-line
+descriptions of all the keywords that can be used in the first input
+file (i.e. ``Ta_param.pod``)
 
 .. list-table::
    :header-rows: 1
@@ -52,7 +59,7 @@ above):
      - INT
      - three integer constants specify boundary conditions
    * - rin
-     - 1.0
+     - 0.5
      - REAL
      - a real number specifies the inner cut-off radius
    * - rcut
@@ -60,46 +67,75 @@ above):
      - REAL
      - a real number specifies the outer cut-off radius
    * - bessel_polynomial_degree
-     - 3
+     - 4
      - INT
      - the maximum degree of Bessel polynomials
    * - inverse_polynomial_degree
-     - 6
+     - 8
      - INT
      - the maximum degree of inverse radial basis functions
+   * - number_of_environment_clusters
+     - 1
+     - INT
+     - the number of clusters for environment-adaptive potentials
+   * - number_of_principal_components
+     - 2
+     - INT
+     - the number of principal components for dimensionality reduction
    * - onebody
      - 1
      - BOOL
      - turns on/off one-body potential
    * - twobody_number_radial_basis_functions
-     - 6
+     - 8
      - INT
      - number of radial basis functions for two-body potential
    * - threebody_number_radial_basis_functions
-     - 5
+     - 6
      - INT
      - number of radial basis functions for three-body potential
-   * - threebody_number_angular_basis_functions
+   * - threebody_angular_degree
      - 5
      - INT
-     - number of angular basis functions for three-body potential
+     - angular degree for three-body potential
-   * - fourbody_snap_twojmax
+   * - fourbody_number_radial_basis_functions
+     - 4
+     - INT
+     - number of radial basis functions for four-body potential
+   * - fourbody_angular_degree
+     - 3
+     - INT
+     - angular degree for four-body potential
+   * - fivebody_number_radial_basis_functions
      - 0
      - INT
-     - band limit for SNAP bispectrum components (0,2,4,6,8... allowed)
+     - number of radial basis functions for five-body potential
-   * - fourbody_snap_chemflag
+   * - fivebody_angular_degree
      - 0
-     - BOOL
+     - INT
-     - turns on/off the explicit multi-element variant of the SNAP bispectrum components
+     - angular degree for five-body potential
-   * - quadratic_pod_potential
+   * - sixbody_number_radial_basis_functions
      - 0
-     - BOOL
+     - INT
-     - turns on/off quadratic POD potential
+     - number of radial basis functions for six-body potential
+   * - sixbody_angular_degree
+     - 0
+     - INT
+     - angular degree for six-body potential
+   * - sevenbody_number_radial_basis_functions
+     - 0
+     - INT
+     - number of radial basis functions for seven-body potential
+   * - sevenbody_angular_degree
+     - 0
+     - INT
+     - angular degree for seven-body potential
+
+Note that both the number of radial basis functions and angular degree
+must decrease as the body order increases. The next table describes all
+keywords that can be used in the second input file (i.e. ``Ta_data.pod``
+in the example above):
 
-All keywords except *species* have default values. If a keyword is not
-set in the input file, its default value is used.  The next table
-describes all keywords that can be used in the second input file
-(i.e. ``Ta_data.pod`` in the example above):
 
 .. list-table::
    :header-rows: 1
@@ -125,6 +161,10 @@ describes all keywords that can be used in the second input file
      - ""
      - STRING
      - specifies the path to test data files in double quotes
+   * - path_to_environment_configuration_set
+     - ""
+     - STRING
+     - specifies the path to environment configuration files in double quotes
    * - fraction_training_data_set
      - 1.0
      - REAL
@@ -133,6 +173,14 @@ describes all keywords that can be used in the second input file
      - 0
      - BOOL
      - turns on/off randomization of the training set
+   * - fraction_test_data_set
+     - 1.0
+     - REAL
+     - a real number (<= 1.0) specifies the fraction of the test set used to validate POD
+   * - randomize_test_data_set
+     - 0
+     - BOOL
+     - turns on/off randomization of the test set
    * - fitting_weight_energy
      - 100.0
      - REAL
@@ -161,6 +209,10 @@ describes all keywords that can be used in the second input file
      - 8
      - INT
      - number of digits after the decimal points for numbers in the coefficient file
+   * - group_weights
+     - global
+     - STRING
+     - ``table`` uses group weights defined for each group named by filename
 
 All keywords except *path_to_training_data_set* have default values. If
 a keyword is not set in the input file, its default value is used.  After
@@ -172,14 +224,44 @@ successful training, a number of output files are produced, if enabled:
 * ``<basename>_test_analysis.pod`` reports detailed errors for all test configurations
 * ``<basename>_coefficients.pod`` contains the coefficients of the POD potential
 
-After training the POD potential, ``Ta_param.pod`` and ``<basename>_coefficients.pod``
+After training the POD potential, ``Ta_param.pod`` and
-are the two files needed to use the POD potential in LAMMPS. See
+``<basename>_coefficients.pod`` are the two files needed to use the POD
-:doc:`pair_style pod <pair_pod>` for using the POD potential. Examples
+potential in LAMMPS.  See :doc:`pair_style pod <pair_pod>` for using the
-about training and using POD potentials are found in the directory
+POD potential. Examples about training and using POD potentials are
-lammps/examples/PACKAGES/pod.
+found in the directory lammps/examples/PACKAGES/pod and the Github repo
+https://github.com/cesmix-mit/pod-examples.
 
-Parameterized Potential Energy Surface
+Loss Function Group Weights
-""""""""""""""""""""""""""""""""""""""
+^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+The *group_weights* keyword in the ``data.pod`` file is responsible for
+weighting certain groups of configurations in the loss function. For
+example:
+
+.. code-block:: LAMMPS
+
+    group_weights table
+    Displaced_A15 100.0 1.0
+    Displaced_BCC 100.0 1.0
+    Displaced_FCC 100.0 1.0
+    Elastic_BCC   100.0 1.0
+    Elastic_FCC   100.0 1.0
+    GSF_110       100.0 1.0
+    GSF_112       100.0 1.0
+    Liquid        100.0 1.0
+    Surface       100.0 1.0
+    Volume_A15    100.0 1.0
+    Volume_BCC    100.0 1.0
+    Volume_FCC    100.0 1.0
+
+This will apply an energy weight of ``100.0`` and a force weight of
+``1.0`` for all groups in the ``Ta`` example. The groups are named by
+their respective filename. If certain groups are left out of this table,
+then the globally defined weights from the ``fitting_weight_energy`` and
+``fitting_weight_force`` keywords will be used.
+
+POD Potential
+"""""""""""""
 
 We consider a multi-element system of *N* atoms with :math:`N_{\rm e}`
 unique elements.  We denote by :math:`\boldsymbol r_n` and :math:`Z_n`
@@ -187,535 +269,82 @@ position vector and type of an atom *n* in the system,
 respectively. Note that we have :math:`Z_n \in \{1, \ldots, N_{\rm e}
 \}`, :math:`\boldsymbol R = (\boldsymbol r_1, \boldsymbol r_2, \ldots,
 \boldsymbol r_N) \in \mathbb{R}^{3N}`, and :math:`\boldsymbol Z = (Z_1,
-Z_2, \ldots, Z_N) \in \mathbb{N}^{N}`. The potential energy surface
+Z_2, \ldots, Z_N) \in \mathbb{N}^{N}`. The total energy of the
-(PES) of the system can be expressed as a many-body expansion of the
+POD potential is expressed as :math:`E(\boldsymbol R, \boldsymbol Z) =
-form
+\sum_{i=1}^N E_i(\boldsymbol R_i, \boldsymbol Z_i)`, where
 
 .. math::
 
-    E(\boldsymbol R, \boldsymbol Z, \boldsymbol{\eta}, \boldsymbol{\mu}) \ = \ & \sum_{i} V^{(1)}(\boldsymbol r_i, Z_i, \boldsymbol \mu^{(1)} ) + \frac12 \sum_{i,j} V^{(2)}(\boldsymbol r_i, \boldsymbol r_j, Z_i, Z_j, \boldsymbol \eta, \boldsymbol \mu^{(2)})  \\
+    E_i(\boldsymbol R_i, \boldsymbol Z_i) \ = \ \sum_{m=1}^M c_m \mathcal{D}_{im}(\boldsymbol R_i, \boldsymbol Z_i)
-    & + \frac16 \sum_{i,j,k} V^{(3)}(\boldsymbol r_i, \boldsymbol r_j, \boldsymbol r_k, Z_i, Z_j, Z_k, \boldsymbol \eta, \boldsymbol \mu^{(3)}) + \ldots
+
-
+
-where :math:`V^{(1)}` is the one-body potential often used for
+Here :math:`c_m` are trainable coefficients and
-representing external field or energy of isolated elements, and the
+:math:`\mathcal{D}_{im}(\boldsymbol R_i, \boldsymbol Z_i)` are per-atom
-higher-body potentials :math:`V^{(2)}, V^{(3)}, \ldots` are symmetric,
+POD descriptors. Summing the per-atom descriptors over :math:`i` yields
-uniquely defined, and zero if two or more indices take identical values.
+the global descriptors :math:`d_m(\boldsymbol R, \boldsymbol Z) =
-The superscript on each potential denotes its body order. Each *q*-body
+\sum_{i=1}^N \mathcal{D}_{im}(\boldsymbol R_i, \boldsymbol Z_i)`.  It
-potential :math:`V^{(q)}` depends on :math:`\boldsymbol \mu^{(q)}` which
+thus follows that :math:`E(\boldsymbol R, \boldsymbol Z) = \sum_{m=1}^M
-are sets of parameters to fit the PES. Note that :math:`\boldsymbol \mu`
+c_m d_m(\boldsymbol R, \boldsymbol Z)`.
-is a collection of all potential parameters :math:`\boldsymbol
+
-\mu^{(1)}`, :math:`\boldsymbol \mu^{(2)}`, :math:`\boldsymbol
+The per-atom POD descriptors include one, two, three, four, five, six,
-\mu^{(3)}`, etc, and that :math:`\boldsymbol \eta` is a set of
+and seven-body descriptors, which can be specified in the first input
-hyper-parameters such as inner cut-off radius :math:`r_{\rm in}` and
+file. Furthermore, the per-atom POD descriptors also depend on the
-outer cut-off radius :math:`r_{\rm cut}`.
+number of environment clusters specified in the first input file.
-
+Please see :ref:`(Nguyen2024) <Nguyen20242a>` and :ref:`(Nguyen and Sema)
-Interatomic potentials rely on parameters to learn relationship between
+<Nguyen20243a>` for the detailed description of the per-atom POD
-atomic environments and interactions.  Since interatomic potentials are
+descriptors.
-approximations by nature, their parameters need to be set to some
-reference values or fitted against data by necessity.  Typically,
-potential fitting finds optimal parameters, :math:`\boldsymbol \mu^*`,
-to minimize a certain loss function of the predicted quantities and
-data. Since the fitted potential depends on the data set used to fit it,
-different data sets will yield different optimal parameters and thus
-different fitted potentials. When fitting the same functional form on
-*Q* different data sets, we would obtain *Q* different optimized
-potentials, :math:`E(\boldsymbol R,\boldsymbol Z, \boldsymbol \eta,
-\boldsymbol \mu_q^*), 1 \le q \le Q`.  Consequently, there exist many
-different sets of optimized parameters for empirical interatomic
-potentials.
-
-Instead of optimizing the potential parameters, inspired by the reduced
-basis method :ref:`(Grepl) <Grepl20072>` for parameterized partial
-differential equations, we view the parameterized PES as a parametric
-manifold of potential energies
-
-.. math::
-
-    \mathcal{M} = \{E(\boldsymbol R, \boldsymbol Z, \boldsymbol \eta, \boldsymbol \mu) \ | \  \boldsymbol \mu \in \Omega^{\boldsymbol \mu} \}
-
-where :math:`\Omega^{\boldsymbol \mu}` is a parameter domain in which
-:math:`\boldsymbol \mu` resides.  The parametric manifold
-:math:`\mathcal{M}` contains potential energy surfaces for all values of
-:math:`\boldsymbol \mu \in \Omega^{\boldsymbol \mu}`.  Therefore, the
-parametric manifold yields a much richer and more transferable atomic
-representation than any particular individual PES :math:`E(\boldsymbol
-R, \boldsymbol Z, \boldsymbol \eta, \boldsymbol \mu^*)`.
-
-We propose specific forms of the parameterized potentials for one-body,
-two-body, and three-body interactions. We apply the Karhunen-Loeve
-expansion to snapshots of the parameterized potentials to obtain sets of
-orthogonal basis functions. These basis functions are aggregated
-according to the chemical elements of atoms, thus leading to
-multi-element proper orthogonal descriptors.
-
-Proper Orthogonal Descriptors
-"""""""""""""""""""""""""""""
-
-Proper orthogonal descriptors are finger prints characterizing the
-radial and angular distribution of a system of atoms. The detailed
-mathematical definition is given in the paper by Nguyen and Rohskopf
-:ref:`(Nguyen) <Nguyen20222>`.
-
-The descriptors for the one-body interaction are used to capture energy
-of isolated elements and defined as follows
-
-.. math::
-
-    D_{ip}^{(1)} =  \left\{
-        \begin{array}{ll}
-        1, & \mbox{if } Z_i = p \\
-        0, & \mbox{if } Z_i \neq p
-        \end{array}
-    \right.
-
-for :math:`1 \le i \le N, 1 \le p \le N_{\rm e}`. The number of one-body
-descriptors per atom is equal to the number of elements. The one-body
-descriptors are independent of atom positions, but dependent on atom
-types. The one-body descriptors are active only when the keyword
-*onebody* is set to 1.
-
-We adopt the usual assumption that the direct interaction between two
-atoms vanishes smoothly when their distance is greater than the outer
-cutoff distance :math:`r_{\rm cut}`. Furthermore, we assume that two
-atoms can not get closer than the inner cutoff distance :math:`r_{\rm
-in}` due to the Pauli repulsion principle. Let :math:`r \in (r_{\rm in},
-r_{\rm cut})`, we introduce the following parameterized radial functions
-
-.. math::
-
-    \phi(r, r_{\rm in}, r_{\rm cut}, \alpha, \beta)  = \frac{\sin (\alpha \pi x) }{r - r_{\rm in}}, \qquad  \varphi(r, \gamma)  = \frac{1}{r^\gamma} ,
-
-where the scaled distance function :math:`x` is defined below to enrich the two-body manifold
-
-.. math::
-
-    x(r, r_{\rm in}, r_{\rm cut}, \beta) = \frac{e^{-\beta(r - r_{\rm in})/(r_{\rm cut} - r_{\rm in})} - 1}{e^{-\beta} - 1} .
-
-We introduce the following function as a convex combination of the two functions
-
-.. math::
-
-    \psi(r, r_{\rm in}, r_{\rm cut}, \alpha, \beta, \gamma, \kappa)  = \kappa \phi(r, r_{\rm in}, r_{\rm cut}, \alpha, \beta) + (1- \kappa)  \varphi(r, \gamma) .
-
-We see that :math:`\psi` is a function of distance :math:`r`, cut-off
-distances :math:`r_{\rm in}` and :math:`r_{\rm cut}`, and parameters
-:math:`\alpha, \beta, \gamma, \kappa`. Together these parameters allow
-the function :math:`\psi` to characterize a diverse spectrum of two-body
-interactions within the cut-off interval :math:`(r_{\rm in}, r_{\rm
-cut})`.
-
-Next, we introduce the following parameterized potential
-
-.. math::
-
-    W^{(2)}(r_{ij}, \boldsymbol \eta, \boldsymbol \mu^{(2)})  = f_{\rm c}(r_{ij}, \boldsymbol \eta) \psi(r_{ij}, \boldsymbol \eta, \boldsymbol \mu^{(2)})
-
-where :math:`\eta_1 = r_{\rm in}, \eta_2 = r_{\rm cut}, \mu_1^{(2)} =
-\alpha, \mu_2^{(2)} = \beta, \mu_3^{(2)} = \gamma`, and
-:math:`\mu_4^{(2)} = \kappa`. Here the cut-off function :math:`f_{\rm
-c}(r_{ij}, \boldsymbol \eta)` proposed in [refs] is used to ensure the
-smooth vanishing of the potential and its derivative for :math:`r_{ij}
-\ge r_{\rm cut}`:
-
-.. math::
-
-    f_{\rm c}(r_{ij},  r_{\rm in}, r_{\rm cut})  =  \exp \left(1 -\frac{1}{\sqrt{\left(1 - \frac{(r-r_{\rm in})^3}{(r_{\rm cut} - r_{\rm in})^3} \right)^2 + 10^{-6}}} \right)
-
-Based on the parameterized potential, we form a set of snapshots as
-follows.  We assume that we are given :math:`N_{\rm s}` parameter tuples
-:math:`\boldsymbol \mu^{(2)}_\ell, 1 \le \ell \le N_{\rm s}`. We
-introduce the following set of snapshots on :math:`(r_{\rm in}, r_{\rm
-cut})`:
-
-.. math::
-
-    \xi_\ell(r_{ij}, \boldsymbol \eta) =  W^{(2)}(r_{ij}, \boldsymbol \eta, \boldsymbol \mu^{(2)}_\ell),  \quad \ell = 1, \ldots, N_{\rm s} .
-
-To ensure adequate sampling of the PES for different parameters, we
-choose :math:`N_{\rm s}` parameter points :math:`\boldsymbol
-\mu^{(2)}_\ell = (\alpha_\ell, \beta_\ell, \gamma_\ell, \kappa_\ell), 1
-\le \ell \le N_{\rm s}` as follows. The parameters :math:`\alpha \in [1,
-N_\alpha]` and :math:`\gamma \in [1, N_\gamma]` are integers, where
-:math:`N_\alpha` and :math:`N_\gamma` are the highest degrees for
-:math:`\alpha` and :math:`\gamma`, respectively. We next choose
-:math:`N_\beta` different values of :math:`\beta` in the interval
-:math:`[\beta_{\min}, \beta_{\max}]`, where :math:`\beta_{\min} = 0` and
-:math:`\beta_{\max} = 4`. The parameter :math:`\kappa` can be set either
-0 or 1.  Hence, the total number of parameter points is :math:`N_{\rm s}
-= N_\alpha N_\beta + N_\gamma`.  Although :math:`N_\alpha, N_\beta,
-N_\gamma` can be chosen conservatively large, we find that
-:math:`N_\alpha = 6, N_\beta = 3, N_\gamma = 8` are adequate for most
-problems.  Note that :math:`N_\alpha` and :math:`N_\gamma` correspond to
-*bessel_polynomial_degree* and *inverse_polynomial_degree*,
-respectively.
-
-We employ the Karhunen-Loeve (KL) expansion to generate an orthogonal
-basis set which is known to be optimal for representation of the
-snapshot family :math:`\{\xi_\ell\}_{\ell=1}^{N_{\rm s}}`. The two-body
-orthogonal basis functions are computed as follows
-
-.. math::
-
-    U^{(2)}_m(r_{ij}, \boldsymbol \eta) = \sum_{\ell = 1}^{N_{\rm s}} A_{\ell m}(\boldsymbol \eta) \,  \xi_\ell(r_{ij}, \boldsymbol \eta), \qquad m = 1, \ldots, N_{\rm 2b} ,
-
-where the matrix :math:`\boldsymbol A \in \mathbb{R}^{N_{\rm s} \times
-N_{\rm s}}` consists of eigenvectors of the eigenvalue problem
-
-.. math::
-
-    \boldsymbol C \boldsymbol a = \lambda \boldsymbol a
-
-with the entries of :math:`\boldsymbol C \in \mathbb{R}^{N_{\rm s} \times N_{\rm s}}` being given by
-
-.. math::
-
-    C_{ij}  = \frac{1}{N_{\rm s}} \int_{r_{\rm in}}^{r_{\rm cut}} \xi_i(x, \boldsymbol \eta) \xi_j(x, \boldsymbol \eta) dx, \quad 1 \le i, j \le N_{\rm s}
-
-Note that the eigenvalues :math:`\lambda_\ell, 1 \le \ell \le N_{\rm
-s}`, are ordered such that :math:`\lambda_1 \ge \lambda_2 \ge \ldots \ge
-\lambda_{N_{\rm s}}`, and that the matrix :math:`\boldsymbol A` is
-pe-computed and stored for any given :math:`\boldsymbol \eta`.  Owing to
-the rapid convergence of the KL expansion, only a small number of
-orthogonal basis functions is needed to obtain accurate
-approximation. The value of :math:`N_{\rm 2b}` corresponds to
-*twobody_number_radial_basis_functions*.
-
-The two-body proper orthogonal descriptors at each atom *i* are computed
-by summing the orthogonal basis functions over the neighbors of atom *i*
-and numerating on the atom types as follows
-
-.. math::
-
-    D^{(2)}_{im l(p, q) }(\boldsymbol \eta)  = \left\{
-    \begin{array}{ll}
-    \displaystyle \sum_{\{j | Z_j = q\}} U^{(2)}_m(r_{ij},  \boldsymbol \eta), & \mbox{if } Z_i = p \\
-    0, & \mbox{if } Z_i \neq p
-    \end{array}
-    \right.
-
-for :math:`1 \le i \le N, 1 \le m \le N_{\rm 2b}, 1 \le q, p \le N_{\rm
-e}`. Here :math:`l(p,q)` is a symmetric index mapping such that
-
-.. math::
-
-    l(p,q)  = \left\{
-    \begin{array}{ll}
-    q + (p-1) N_{\rm e} - p(p-1)/2, & \mbox{if } q \ge p \\
-    p + (q-1) N_{\rm e} - q(q-1)/2, & \mbox{if } q < p .
-    \end{array}
-    \right.
-
-The number of two-body descriptors per atom is thus :math:`N_{\rm 2b}
-N_{\rm e}(N_{\rm e}+1)/2`.
-
-It is important to note that the orthogonal basis functions do not
-depend on the atomic numbers :math:`Z_i` and :math:`Z_j`. Therefore, the
-cost of evaluating the basis functions and their derivatives with
-respect to :math:`r_{ij}` is independent of the number of elements
-:math:`N_{\rm e}`. Consequently, even though the two-body proper
-orthogonal descriptors depend on :math:`\boldsymbol Z`, their
-computational complexity is independent of :math:`N_{\rm e}`.
-
-In order to provide proper orthogonal descriptors for three-body
-interactions, we need to introduce a three-body parameterized
-potential. In particular, the three-body potential is defined as a
-product of radial and angular functions as follows
-
-.. math::
-
-    W^{(3)}(r_{ij}, r_{ik}, \theta_{ijk}, \boldsymbol \eta, \boldsymbol \mu^{(3)})  =  \psi(r_{ij}, r_{\rm min}, r_{\rm max}, \alpha, \beta, \gamma, \kappa) f_{\rm c}(r_{ij}, r_{\rm min}, r_{\rm max}) \\
-    \psi(r_{ik}, r_{\rm min}, r_{\rm max}, \alpha, \beta, \gamma, \kappa) f_{\rm c}(r_{ik}, r_{\rm min}, r_{\rm max}) \\
-    \cos (\sigma \theta_{ijk} + \zeta)
-
-where :math:`\sigma` is the periodic multiplicity, :math:`\zeta` is the
-equilibrium angle, :math:`\boldsymbol \mu^{(3)} = (\alpha, \beta,
-\gamma, \kappa, \sigma, \zeta)`. The three-body potential provides an
-angular fingerprint of the atomic environment through the bond angles
-:math:`\theta_{ijk}` formed with each pair of neighbors :math:`j` and
-:math:`k`.  Compared to the two-body potential, the three-body potential
-has two extra parameters :math:`(\sigma, \zeta)` associated with the
-angular component.
-
-Let :math:`\boldsymbol \varrho = (\alpha, \beta, \gamma, \kappa)`. We
-assume that we are given :math:`L_{\rm r}` parameter tuples
-:math:`\boldsymbol \varrho_\ell, 1 \le \ell \le L_{\rm r}`.  We
-introduce the following set of snapshots on :math:`(r_{\min},
-r_{\max})`:
-
-.. math::
-
-    \zeta_\ell(r_{ij}, r_{\rm min}, r_{\rm max} ) =  \psi(r_{ij}, r_{\rm min}, r_{\rm max}, \boldsymbol \varrho_\ell) f_{\rm c}(r_{ij}, r_{\rm min},  r_{\rm max}), \quad 1 \le \ell \le L_{\rm r} .
-
-We apply the Karhunen-Loeve (KL) expansion to this set of snapshots to
-obtain orthogonal basis functions as follows
-
-.. math::
-
-    U^{r}_m(r_{ij}, r_{\rm min}, r_{\rm max} ) = \sum_{\ell = 1}^{L_{\rm r}} A_{\ell m} \,  \zeta_\ell(r_{ij}, r_{\rm min}, r_{\rm max} ), \qquad m = 1, \ldots, N_{\rm r} ,
-
-where the matrix :math:`\boldsymbol A \in \mathbb{R}^{L_{\rm r} \times L_{\rm r}}` consists
-of eigenvectors of the eigenvalue problem. For the parameterized angular function,
-we consider angular basis functions
-
-.. math::
-
-    U^{a}_n(\theta_{ijk}) = \cos ((n-1) \theta_{ijk}), \qquad  n = 1,\ldots, N_{\rm a},
-
-where :math:`N_{\rm a}` is the number of angular basis functions. The orthogonal
-basis functions for the parameterized potential are computed as follows
-
-.. math::
-
-    U^{(3)}_{mn}(r_{ij}, r_{ik}, \theta_{ijk}, \boldsymbol \eta) = U^{r}_m(r_{ij}, \boldsymbol \eta) U^{r}_m(r_{ik}, \boldsymbol \eta) U^{a}_n(\theta_{ijk}),
-
-for :math:`1 \le m \le N_{\rm r}, 1 \le n \le N_{\rm a}`. The number of three-body
-orthogonal basis functions is equal to :math:`N_{\rm 3b} = N_{\rm r} N_{\rm a}` and
-independent of the number of elements. The value of :math:`N_{\rm r}` corresponds to
-*threebody_number_radial_basis_functions*, while that of :math:`N_{\rm a}` to
-*threebody_number_angular_basis_functions*.
-
-The three-body proper orthogonal descriptors at each atom *i*
-are obtained by summing over the neighbors *j* and *k* of atom *i* as
-
-.. math::
-
-    D^{(3)}_{imn \ell(p, q, s)}(\boldsymbol \eta)  = \left\{
-    \begin{array}{ll}
-    \displaystyle \sum_{\{j | Z_j = q\}} \sum_{\{k | Z_k = s\}} U^{(3)}_{mn}(r_{ij}, r_{ik}, \theta_{ijk}, \boldsymbol \eta), & \mbox{if } Z_i = p \\
-    0, & \mbox{if } Z_i \neq p
-    \end{array}
-    \right.
-
-for :math:`1 \le i \le N, 1 \le m \le N_{\rm r}, 1 \le n \le N_{\rm a}, 1 \le q, p, s \le N_{\rm e}`,
-where
-
-.. math::
-
-    \ell(p,q,s)  = \left\{
-    \begin{array}{ll}
-    s + (q-1) N_{\rm e} - q(q-1)/2 + (p-1)N_{\rm e}(1+N_{\rm e})/2 , & \mbox{if } s \ge q \\
-    q + (s-1) N_{\rm e} - s(s-1)/2 + (p-1)N_{\rm e}(1+N_{\rm e})/2, & \mbox{if } s < q .
-    \end{array}
-    \right.
-
-The number of three-body descriptors per atom is thus :math:`N_{\rm 3b} N_{\rm e}^2(N_{\rm e}+1)/2`.
-While the number of three-body PODs is cubic function of the number of elements,
-the computational complexity of the three-body PODs is independent of the number of elements.
-
-Four-Body SNAP Descriptors
-""""""""""""""""""""""""""
-
-In addition to the proper orthogonal descriptors described above, we also employ
-the spectral neighbor analysis potential (SNAP) descriptors. SNAP uses bispectrum components
-to characterize the local neighborhood of each atom in a very general way. The mathematical definition
-of the bispectrum calculation and its derivatives w.r.t. atom positions is described in
-:doc:`compute snap <compute_sna_atom>`. In SNAP, the
-total energy is decomposed into a sum over atom energies. The energy of
-atom *i* is expressed as a weighted sum over bispectrum components.
-
-.. math::
-
-   E_i^{\rm SNAP} = \sum_{k=1}^{N_{\rm 4b}} \sum_{p=1}^{N_{\rm e}} c_{kp}^{(4)} D_{ikp}^{(4)}
-
-
-where the SNAP descriptors are related to the bispectrum components by
-
-.. math::
-
-    D^{(4)}_{ikp}  = \left\{
-    \begin{array}{ll}
-    \displaystyle B_{ik}, & \mbox{if } Z_i = p \\
-    0, & \mbox{if } Z_i \neq p
-    \end{array}
-    \right.
-
-Here :math:`B_{ik}` is the *k*\ -th bispectrum component of atom *i*. The number of
-bispectrum components :math:`N_{\rm 4b}` depends on the value of *fourbody_snap_twojmax* :math:`= 2 J_{\rm max}`
-and *fourbody_snap_chemflag*. If *fourbody_snap_chemflag* = 0
-then :math:`N_{\rm 4b} = (J_{\rm max}+1)(J_{\rm max}+2)(J_{\rm max}+1.5)/3`.
-If *fourbody_snap_chemflag* = 1 then :math:`N_{\rm 4b} = N_{\rm e}^3 (J_{\rm max}+1)(J_{\rm max}+2)(J_{\rm max}+1.5)/3`.
-The bispectrum calculation is described in more detail in :doc:`compute sna/atom <compute_sna_atom>`.
-
-Linear Proper Orthogonal Descriptor Potentials
-""""""""""""""""""""""""""""""""""""""""""""""
-
-The proper orthogonal descriptors and SNAP descriptors are used to define the atomic energies
-in the following expansion
-
-.. math::
-
-    E_{i}(\boldsymbol \eta) = \sum_{p=1}^{N_{\rm e}} c^{(1)}_p D^{(1)}_{ip} + \sum_{m=1}^{N_{\rm 2b}}  \sum_{l=1}^{N_{\rm e}(N_{\rm e}+1)/2} c^{(2)}_{ml} D^{(2)}_{iml}(\boldsymbol \eta) + \sum_{m=1}^{N_{\rm r}} \sum_{n=1}^{N_{\rm a}}  \sum_{\ell=1}^{N_{\rm e}^2(N_{\rm e}+1)/2} c^{(3)}_{mn\ell} D^{(3)}_{imn\ell}(\boldsymbol \eta) + \sum_{k=1}^{N_{\rm 4b}} \sum_{p=1}^{N_{\rm e}} c_{kp}^{(4)} D_{ikp}^{(4)}(\boldsymbol \eta),
-
-where :math:`D^{(1)}_{ip}, D^{(2)}_{iml}, D^{(3)}_{imn\ell}, D^{(4)}_{ikp}` are the  one-body, two-body, three-body, four-body descriptors,
-respectively, and :math:`c^{(1)}_p, c^{(2)}_{ml}, c^{(3)}_{mn\ell}, c^{(4)}_{kp}` are their respective expansion
-coefficients. In a more compact notation that implies summation over descriptor indices
-the atomic energies can be written as
-
-.. math::
-
-    E_i(\boldsymbol \eta) =  \sum_{m=1}^{N_{\rm e}} c^{(1)}_m D^{(1)}_{im} +  \sum_{m=1}^{N_{\rm d}^{(2)}} c^{(2)}_k D^{(2)}_{im} + \sum_{m=1}^{N_{\rm d}^{(3)}} c^{(3)}_m D^{(3)}_{im} + \sum_{m=1}^{N_{\rm d}^{(4)}} c^{(4)}_m D^{(4)}_{im}
-
-where :math:`N_{\rm d}^{(2)} = N_{\rm 2b} N_{\rm e} (N_{\rm e}+1)/2`,
-:math:`N_{\rm d}^{(3)} = N_{\rm 3b} N_{\rm e}^2 (N_{\rm e}+1)/2`, and
-:math:`N_{\rm d}^{(4)} = N_{\rm 4b} N_{\rm e}` are
-the number of two-body, three-body, and four-body descriptors, respectively.
-
-The potential energy is then obtained by summing local atomic energies :math:`E_i`
-for all atoms :math:`i` in the system
-
-.. math::
-
-    E(\boldsymbol \eta) = \sum_{i}^N E_{i}(\boldsymbol \eta)
-
-Because the descriptors are one-body, two-body, and three-body terms,
-the resulting POD potential is a three-body PES. We can express the potential
-energy as a linear combination of the global descriptors as follows
-
-.. math::
-
-    E(\boldsymbol \eta) = \sum_{m=1}^{N_{\rm e}} c^{(1)}_m d^{(1)}_{m} +  \sum_{m=1}^{N_{\rm d}^{(2)}} c^{(2)}_m d^{(2)}_{m} + \sum_{m=1}^{N_{\rm d}^{(3)}} c^{(3)}_m d^{(3)}_{m} + \sum_{m=1}^{N_{\rm d}^{(4)}} c^{(4)}_m d^{(4)}_{m}
-
-where  the global descriptors are given by
-
-.. math::
-
-    d_{m}^{(1)}(\boldsymbol \eta) = \sum_{i=1}^N D_{im}^{(1)}(\boldsymbol \eta), \quad d_{m}^{(2)}(\boldsymbol \eta) = \sum_{i=1}^N D_{im}^{(2)}(\boldsymbol \eta), \quad d_{m}^{(3)}(\boldsymbol \eta) = \sum_{i=1}^N D_{im}^{(3)}(\boldsymbol \eta), \quad d_{m}^{(4)}(\boldsymbol \eta) = \sum_{i=1}^N D_{im}^{(4)}(\boldsymbol \eta)
-
-Hence, we obtain the atomic forces as
-
-.. math::
-
-    \boldsymbol F = -\nabla E(\boldsymbol \eta) = - \sum_{m=1}^{N_{\rm d}^{(2)}}  c^{(2)}_m  \nabla d_m^{(2)} - \sum_{m=1}^{N_{\rm d}^{(3)}}  c^{(3)}_m \nabla d_m^{(3)} - \sum_{m=1}^{N_{\rm d}^{(4)}}  c^{(4)}_m \nabla d_m^{(4)}
-
-where :math:`\nabla d_m^{(2)}`, :math:`\nabla d_m^{(3)}` and :math:`\nabla d_m^{(4)}` are derivatives of the two-body
-three-body, and four-body global descriptors with respect to atom positions, respectively.
-Note that since the first-body global descriptors are constant, their derivatives are zero.
-
-Quadratic Proper Orthogonal Descriptor Potentials
-"""""""""""""""""""""""""""""""""""""""""""""""""
-
-We recall two-body PODs :math:`D^{(2)}_{ik}, 1 \le k \le N_{\rm d}^{(2)}`,
-and three-body PODs :math:`D^{(3)}_{im}, 1 \le m \le N_{\rm d}^{(3)}`,
-with :math:`N_{\rm d}^{(2)} = N_{\rm 2b} N_{\rm e} (N_{\rm e}+1)/2` and
-:math:`N_{\rm d}^{(3)} = N_{\rm 3b} N_{\rm e}^2 (N_{\rm e}+1)/2` being
-the number of descriptors per atom for the two-body PODs and three-body PODs,
-respectively. We employ them to define a new set of atomic descriptors as follows
-
-.. math::
-
-    D^{(2*3)}_{ikm} = \frac{1}{2N}\left( D^{(2)}_{ik} \sum_{j=1}^N D^{(3)}_{jm} + D^{(3)}_{im} \sum_{j=1}^N D^{(2)}_{jk}  \right)
-
-for :math:`1 \le i \le N, 1 \le k \le N_{\rm d}^{(2)}, 1 \le m \le N_{\rm d}^{(3)}`.
-The new descriptors are four-body because they involve central atom :math:`i` together
-with three neighbors :math:`j, k` and :math:`l`. The total number of new  descriptors per atom is equal to
-
-.. math::
-
-    N_{\rm d}^{(2*3)} = N_{\rm d}^{(2)} * N_{\rm d}^{(3)} = N_{\rm 2b} N_{\rm 3b} N_{\rm e}^3 (N_{\rm e}+1)^2/4 .
-
-The new global descriptors are calculated as
-
-.. math::
-
-    d^{(2*3)}_{km} = \sum_{i=1}^N D^{(2*3)}_{ikm} = \left( \sum_{i=1}^N D^{(2)}_{ik} \right) \left( \sum_{i=1}^N D^{(3)}_{im} \right) = d^{(2)}_{k} d^{(3)}_m,
-
-for :math:`1 \le k \le N_{\rm d}^{(2)}, 1 \le m \le N_{\rm d}^{(3)}`. Hence, the gradient
-of the new global descriptors with respect to atom positions is calculated as
-
-.. math::
-
-    \nabla d^{(2*3)}_{km} = d^{(3)}_m \nabla d^{(2)}_{k}  +  d^{(2)}_{k} \nabla d^{(3)}_m, \quad 1 \le k \le N_{\rm d}^{(2)}, 1 \le m \le N_{\rm d}^{(3)} .
-
-The quadratic  POD potential is defined as a linear combination of the
-original and new global descriptors as follows
-
-.. math::
-
-    E^{(2*3)} = \sum_{k=1}^{N_{\rm 2d}^{(2*3)}} \sum_{m=1}^{N_{\rm 3d}^{(2*3)}} c^{(2*3)}_{km} d^{(2*3)}_{km} .
-
-It thus follows that
-
-.. math::
-
-    E^{(2*3)} = 0.5 \sum_{k=1}^{N_{\rm 2d}^{(2*3)}} \left( \sum_{m=1}^{N_{\rm 3d}^{(2*3)}} c^{(2*3)}_{km} d_m^{(3)} \right) d_k^{(2)} + 0.5 \sum_{m=1}^{N_{\rm 3d}^{(2*3)}} \left( \sum_{k=1}^{N_{\rm 2d}^{(2*3)}} c^{(2*3)}_{km} d_k^{(2)} \right) d_m^{(3)}  ,
-
-which is simplified to
-
-.. math::
-
-    E^{(2*3)} =  0.5 \sum_{k=1}^{N_{\rm 2d}^{(2*3)}} b_k^{(2)} d_k^{(2)} +  0.5 \sum_{m=1}^{N_{\rm 3d}^{(2*3)}}   b_m^{(3)} d_m^{(3)}
-
-where
-
-.. math::
-
-    b_k^{(2)} & = \sum_{m=1}^{N_{\rm 3d}^{(2*3)}} c^{(2*3)}_{km} d_m^{(3)}, \quad k = 1,\ldots, N_{\rm 2d}^{(2*3)}, \\
-    b_m^{(3)} & = \sum_{k=1}^{N_{\rm 2d}^{(2*3)}} c^{(2*3)}_{km} d_k^{(2)}, \quad m = 1,\ldots, N_{\rm 3d}^{(2*3)} .
-
-The quadratic POD potential results in the following atomic forces
-
-.. math::
-
-    \boldsymbol F^{(2*3)} = - \sum_{k=1}^{N_{\rm 2d}^{(2*3)}} \sum_{m=1}^{N_{\rm 3d}^{(2*3)}} c^{(2*3)}_{km}  \nabla d^{(2*3)}_{km} .
-
-It can be shown that
-
-.. math::
-
-    \boldsymbol F^{(2*3)} = - \sum_{k=1}^{N_{\rm 2d}^{(2*3)}}   b^{(2)}_k \nabla d_k^{(2)} - \sum_{m=1}^{N_{\rm 3d}^{(2*3)}}  b^{(3)}_m  \nabla d_m^{(3)} .
-
-The calculation of the atomic forces for the quadratic POD  potential
-only requires the extra calculation of :math:`b_k^{(2)}` and :math:`b_m^{(3)}` which can be negligible.
-As a result, the quadratic  POD potential does not increase the computational complexity.
-
 
 Training
 """"""""
 
-POD potentials are trained using the least-squares regression against
+A POD potential is trained using the least-squares regression against
 density functional theory (DFT) data.  Let :math:`J` be the number of
 training configurations, with :math:`N_j` being the number of atoms in
-the j-th configuration. Let :math:`\{E^{\star}_j\}_{j=1}^{J}` and
+the j-th configuration. The training configurations are extracted from
-:math:`\{\boldsymbol F^{\star}_j\}_{j=1}^{J}` be the DFT energies and
+the extended XYZ files located in a directory (i.e.,
-forces for :math:`J` configurations. Next, we calculate the global
+path_to_training_data_set in the second input file).  Let
-descriptors and their derivatives for all training configurations. Let
+:math:`\{E^{\star}_j\}_{j=1}^{J}` and :math:`\{\boldsymbol
-:math:`d_{jm}, 1 \le m \le M`, be the global descriptors associated with
+F^{\star}_j\}_{j=1}^{J}` be the DFT energies and forces for :math:`J`
-the j-th configuration, where :math:`M` is the number of global
+configurations. Next, we calculate the global descriptors and their
-descriptors. We then form a matrix :math:`\boldsymbol A \in
+derivatives for all training configurations. Let :math:`d_{jm}, 1 \le m
-\mathbb{R}^{J \times M}` with entries :math:`A_{jm} = d_{jm}/ N_j` for
+\le M`, be the global descriptors associated with the j-th
-:math:`j=1,\ldots,J` and :math:`m=1,\ldots,M`.  Moreover, we form a
+configuration, where :math:`M` is the number of global descriptors. We
-matrix :math:`\boldsymbol B \in \mathbb{R}^{\mathcal{N} \times M}` by
+then form a matrix :math:`\boldsymbol A \in \mathbb{R}^{J \times M}`
-stacking the derivatives of the global descriptors for all training
+with entries :math:`A_{jm} = d_{jm}/ N_j` for :math:`j=1,\ldots,J` and
-configurations from top to bottom, where :math:`\mathcal{N} =
+:math:`m=1,\ldots,M`.  Moreover, we form a matrix :math:`\boldsymbol B
-3\sum_{j=1}^{J} N_j`.
+\in \mathbb{R}^{\mathcal{N} \times M}` by stacking the derivatives of
+the global descriptors for all training configurations from top to
+bottom, where :math:`\mathcal{N} = 3\sum_{j=1}^{J} N_j`.
 
 The coefficient vector :math:`\boldsymbol c` of the POD potential is
 found by solving the following least-squares problem
 
 .. math::
 
-    {\min}_{\boldsymbol c \in \mathbb{R}^{M}} \ w_E \|\boldsymbol A(\boldsymbol \eta) \boldsymbol c - \bar{\boldsymbol E}^{\star} \|^2 + w_F \|\boldsymbol B(\boldsymbol \eta) \boldsymbol c + \boldsymbol F^{\star} \|^2 + w_R \|\boldsymbol c \|^2,
+    {\min}_{\boldsymbol c \in \mathbb{R}^{M}} \ w_E \|\boldsymbol A \boldsymbol c - \bar{\boldsymbol E}^{\star} \|^2 + w_F \|\boldsymbol B \boldsymbol c + \boldsymbol F^{\star} \|^2 + w_R \|\boldsymbol c \|^2,
 
 where :math:`w_E` and :math:`w_F` are weights for the energy
 (*fitting_weight_energy*) and force (*fitting_weight_force*),
-respectively; and :math:`w_R` is the regularization parameter (*fitting_regularization_parameter*).  Here :math:`\bar{\boldsymbol E}^{\star} \in
+respectively; and :math:`w_R` is the regularization parameter
-\mathbb{R}^{J}` is a vector of with entries :math:`\bar{E}^{\star}_j =
+(*fitting_regularization_parameter*).  Here :math:`\bar{\boldsymbol
-E^{\star}_j/N_j` and :math:`\boldsymbol F^{\star}` is a vector of
+E}^{\star} \in \mathbb{R}^{J}` is a vector of with entries
-:math:`\mathcal{N}` entries obtained by stacking :math:`\{\boldsymbol
+:math:`\bar{E}^{\star}_j = E^{\star}_j/N_j` and :math:`\boldsymbol
-F^{\star}_j\}_{j=1}^{J}` from top to bottom.
+F^{\star}` is a vector of :math:`\mathcal{N}` entries obtained by
+stacking :math:`\{\boldsymbol F^{\star}_j\}_{j=1}^{J}` from top to
+bottom.
 
-The training procedure is the same for both the linear and quadratic POD
+Validation
-potentials.  However, since the quadratic POD potential has a
+""""""""""
-significantly larger number of the global descriptors, it is more
-expensive to train the linear POD potential. This is because the
-training of the quadratic POD potential still requires us to calculate
-and store the quadratic global descriptors and their
-gradient. Furthermore, the quadratic POD potential may require more
-training data in order to prevent over-fitting. In order to reduce the
-computational cost of fitting the quadratic POD potential and avoid
-over-fitting, we can use subsets of two-body and three-body PODs for
-constructing the new descriptors.
 
+POD potential can be validated on a test dataset in a directory
+specified by setting path_to_test_data_set in the second input file.  It
+is possible to validate the POD potential after the training is
+complete.  This is done by providing the coefficient file as an input to
+:doc:`fitpod <fitpod_command>`, for example,
+
+.. code-block:: LAMMPS
+
+   fitpod Ta_param.pod Ta_data.pod Ta_coefficients.pod
 
 Restrictions
 """"""""""""
@@ -727,7 +356,11 @@ LAMMPS was built with that package. See the :doc:`Build package
 Related commands
 """"""""""""""""
 
-:doc:`pair_style pod <pair_pod>`
+:doc:`pair_style pod <pair_pod>`,
+:doc:`compute pod/atom <compute_pod_atom>`,
+:doc:`compute podd/atom <compute_pod_atom>`,
+:doc:`compute pod/local <compute_pod_atom>`,
+:doc:`compute pod/global <compute_pod_atom>`
 
 Default
 """""""
@@ -736,10 +369,20 @@ The keyword defaults are also given in the description of the input files.
 
 ----------
 
-.. _Grepl20072:
+.. _Nguyen20222a:
 
-**(Grepl)** Grepl, Maday, Nguyen, and Patera, ESAIM: Mathematical Modelling and Numerical Analysis 41(3), 575-605, (2007).
+**(Nguyen and Rohskopf)** Nguyen and Rohskopf,  Journal of Computational Physics, 480, 112030, (2023).
+
+.. _Nguyen20232a:
+
+**(Nguyen2023)** Nguyen, Physical Review B, 107(14), 144103, (2023).
+
+.. _Nguyen20242a:
+
+**(Nguyen2024)** Nguyen, Journal of Computational Physics, 113102, (2024).
+
+.. _Nguyen20243a:
+
+**(Nguyen and Sema)** Nguyen and Sema, https://arxiv.org/abs/2405.00306, (2024).
 
-.. _Nguyen20222:
 
-**(Nguyen)** Nguyen and Rohskopf, arXiv preprint arXiv:2209.02362 (2022).

doc/src/fix_ipi.rst

@@ -80,7 +80,7 @@ Obtaining i-PI
 """"""""""""""
 
 Here are the commands to set up a virtual environment and install
-i-PI into it with all its dependencies via the PyPi repository and
+i-PI into it with all its dependencies via the PyPI repository and
 the pip package manager.
 
 .. code-block:: sh

doc/src/labelmap.rst

@@ -44,8 +44,8 @@ The label map can also be defined by the :doc:`read_data <read_data>`
 command when it reads these sections in a data file: Atom Type Labels,
 Bond Type Labels, etc.  See the :doc:`Howto type labels
 <Howto_type_labels>` doc page for a general discussion of how type
-labels can be used.  See :ref:`(Gissinger) <Typelabel>` for a discussion
+labels can be used.  See :ref:`(Gissinger) <Typelabel1>` for a
-of the type label implementation in LAMMPS and its uses.
+discussion of the type label implementation in LAMMPS and its uses.
 
 Valid type labels can contain any alphanumeric character, but must not
 start with a number, a '#', or a '*' character.  They can contain other
@@ -103,6 +103,6 @@ none
 
 -----------
 
-.. _Typelabel:
+.. _Typelabel1:
 
 **(Gissinger)** J. R. Gissinger, I. Nikiforov, Y. Afshar, B. Waters, M. Choi, D. S. Karls, A. Stukowski, W. Im, H. Heinz, A. Kohlmeyer, and E. B. Tadmor, J Phys Chem B, 128, 3282-3297 (2024).

doc/src/pair_charmm.rst

@@ -112,26 +112,22 @@ Description
 These pair styles compute Lennard Jones (LJ) and Coulombic
 interactions with additional switching or shifting functions that ramp
 the energy and/or force smoothly to zero between an inner and outer
-cutoff.  They are implementations of the widely used CHARMM force
+cutoff.  They implement the widely used CHARMM force field, see
-field used in the `CHARMM <https://www.charmm.org>`_ MD code (and
+:doc:`Howto discussion on biomolecular force fields <Howto_bioFF>` for
-others).  See :ref:`(MacKerell) <pair-MacKerell>` for a description of the
+details.
-CHARMM force field.
 
 The styles with *charmm* (not *charmmfsw* or *charmmfsh*\ ) in their
 name are the older, original LAMMPS implementations.  They compute the
-LJ and Coulombic interactions with an energy switching function (esw,
+LJ and Coulombic interactions with an energy switching function which
-shown in the formula below as S(r)), which ramps the energy smoothly
+ramps the energy smoothly to zero between the inner and outer cutoff.
-to zero between the inner and outer cutoff.  This can cause
+This can cause irregularities in pairwise forces (due to the discontinuous
-irregularities in pairwise forces (due to the discontinuous second
+second derivative of energy at the boundaries of the switching region),
-derivative of energy at the boundaries of the switching region), which
+which in some cases can result in detectable artifacts in an MD simulation.
-in some cases can result in detectable artifacts in an MD simulation.
 
 The newer styles with *charmmfsw* or *charmmfsh* in their name replace
 the energy switching with force switching (fsw) and force shifting
 (fsh) functions, for LJ and Coulombic interactions respectively.
-These follow the formulas and description given in
+
-:ref:`(Steinbach) <Steinbach>` and :ref:`(Brooks) <Brooks1>` to minimize these
-artifacts.
 
 .. note::
 
@@ -152,26 +148,6 @@ artifacts.
    the CHARMM force field energies and forces, when using one of these
    two CHARMM pair styles.
 
-.. math::
-
-   E = & LJ(r) \qquad \qquad \qquad r < r_{\rm in} \\
-     = & S(r) * LJ(r) \qquad \qquad r_{\rm in} < r < r_{\rm out} \\
-     = & 0 \qquad \qquad \qquad \qquad r > r_{\rm out} \\
-   E = & C(r) \qquad \qquad \qquad r < r_{\rm in} \\
-     = & S(r) * C(r) \qquad \qquad r_{\rm in} < r < r_{\rm out} \\
-     = & 0 \qquad \qquad \qquad \qquad r > r_{\rm out} \\
-   LJ(r) = & 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} -
-           \left(\frac{\sigma}{r}\right)^6 \right] \\
-   C(r) = & \frac{C q_i q_j}{ \epsilon r} \\
-   S(r) = & \frac{ \left[r_{\rm out}^2 - r^2\right]^2
-     \left[r_{\rm out}^2 + 2r^2 - 3{r_{\rm in}^2}\right]}
-   { \left[r_{\rm out}^2 - {r_{\rm in}}^2\right]^3 }
-
-where S(r) is the energy switching function mentioned above for the
-*charmm* styles.  See the :ref:`(Steinbach) <Steinbach>` paper for the
-functional forms of the force switching and force shifting functions
-used in the *charmmfsw* and *charmmfsh* styles.
-
 When using the *lj/charmm/coul/charmm styles*, both the LJ and
 Coulombic terms require an inner and outer cutoff. They can be the
 same for both formulas or different depending on whether 2 or 4

doc/src/pair_dpd_coul_slater_long.rst

@@ -13,16 +13,11 @@ Syntax
 
    pair_style dpd/coul/slater/long T cutoff_DPD seed lambda cutoff_coul
 
-   pair_coeff I J a_IJ Gamma is_charged
+* T = temperature (temperature units)
-
-* T = temperature (temperature units) (dpd only)
 * cutoff_DPD = global cutoff for DPD interactions (distance units)
 * seed = random # seed (positive integer)
 * lambda = decay length of the charge (distance units)
-* cutoff_coul = real part cutoff for Coulombic interactions (distance units)
+* cutoff_coul = global cutoff for Coulombic interactions (distance units)
-* I,J = numeric atom types, or type labels
-* Gamma = DPD Gamma coefficient
-* is_charged (boolean) set to yes if I and J are charged beads
 
 Examples
 """"""""
@@ -30,66 +25,90 @@ Examples
 .. code-block:: LAMMPS
 
    pair_style dpd/coul/slater/long 1.0 2.5 34387 0.25 3.0
-   pair_coeff 1 1 78.0 4.5 # not charged by default
+
+   pair_coeff 1 1 78.0 4.5          # not charged by default
    pair_coeff 2 2 78.0 4.5 yes
 
 
 Description
 """""""""""
 
-.. versionadded:: TBD
+.. versionadded:: 27June2024
 
-Style *dpd/coul/slater/long* computes a force field for dissipative particle dynamics
+Style *dpd/coul/slater/long* computes a force field for dissipative
-(DPD) following the exposition in :ref:`(Groot) <Groot5>` with the addition of
+particle dynamics (DPD) following the exposition in :ref:`(Groot)
-electrostatic interactions. The coulombic forces in mesoscopic models
+<Groot5>`.  It also allows for the use of charged particles in the
-employ potentials without explicit excluded-volume interactions.
+model by adding a long-range Coulombic term to the DPD interactions.
-The goal is to prevent artificial ionic pair formation by including a charge
+The short-range portion of the Coulombics is calculated by this pair
-distribution in the Coulomb potential, following the formulation of
+style.  The long-range Coulombics are computed by use of the
-:ref:`(Melchor) <Melchor1>`:
+:doc:`kspace_style <kspace_style>` command, e.g. using the Ewald or
+PPPM styles.
 
-The force on bead I due to bead J is given as a sum
+Coulombic forces in mesoscopic models such as DPD employ potentials
-of 4 terms
+without explicit excluded-volume interactions.  The goal is to prevent
+artificial ionic pair formation by including a charge distribution in
+the Coulomb potential, following the formulation in :ref:`(Melchor1)
+<Melchor1>`.
+
+.. note::
+
+   This pair style is effectively the combination of the
+   :doc:`pair_style dpd <pair_dpd>` and :doc:`pair_style
+   coul/slater/long <pair_coul_slater>` commands, but should be more
+   efficient (especially on GPUs) than using :doc:`pair_style
+   hybrid/overlay dpd coul/slater/long <pair_hybrid>`. That is
+   particularly true for the GPU package version of the pair style since
+   this version is compatible with computing neighbor lists on the GPU
+   instead of the CPU as is required for hybrid styles.
+
+In the charged DPD model, the force on bead I due to bead J is given
+as a sum of 4 terms:
 
 .. math::
 
    \vec{f}  = & (F^C + F^D + F^R + F^E) \hat{r_{ij}} \\
-   F^C      = & A w(r) \qquad \qquad \qquad \qquad \qquad r < r_c \\
+   F^C      = & A w(r) \qquad \qquad \qquad \qquad \qquad r < r_{DPD} \\
-   F^D      = & - \gamma w^2(r) (\hat{r_{ij}} \bullet \vec{v}_{ij}) \qquad \qquad r < r_c \\
+   F^D      = & - \gamma w^2(r) (\hat{r_{ij}} \bullet \vec{v}_{ij}) \qquad \qquad r < r_{DPD} \\
-   F^R      = & \sigma w(r) \alpha (\Delta t)^{-1/2} \qquad \qquad \qquad r < r_c \\
+   F^R      = & \sigma w(r) \alpha (\Delta t)^{-1/2} \qquad \qquad \qquad r < r_{DPD} \\
-   w(r)     = & 1 - \frac{r}{r_c} \\
+   w(r)     = & 1 - \frac{r}{r_{DPD}} \\
-   F^E      = & \frac{Cq_iq_j}{\epsilon r^2} \left( 1- exp\left( \frac{2r_{ij}}{\lambda} \right) \left( 1 + \frac{2r_{ij}}{\lambda} \left( 1 + \frac{r_{ij}}{\lambda} \right)\right) \right)
+   F^E      = & \frac{C q_iq_j}{\epsilon r^2} \left( 1- exp\left( \frac{2r_{ij}}{\lambda} \right) \left( 1 + \frac{2r_{ij}}{\lambda} \left( 1 + \frac{r_{ij}}{\lambda} \right)\right) \right)
 
-where :math:`F^C` is a conservative force, :math:`F^D` is a dissipative
+where :math:`F^C` is a conservative force, :math:`F^D` is a
-force, :math:`F^R` is a random force, and :math:`F^E` is an electrostatic force.
+dissipative force, :math:`F^R` is a random force, and :math:`F^E` is
-:math:`\hat{r_{ij}}` is a unit vector in the direction
+an electrostatic force.  :math:`\hat{r_{ij}}` is a unit vector in the
-:math:`r_i - r_j`, :math:`\vec{v}_{ij}` is
+direction :math:`r_i - r_j`, :math:`\vec{v}_{ij}` is the vector
-the vector difference in velocities of the two atoms :math:`\vec{v}_i -
+difference in velocities of the two atoms :math:`\vec{v}_i -
 \vec{v}_j`, :math:`\alpha` is a Gaussian random number with zero mean
 and unit variance, *dt* is the timestep size, and :math:`w(r)` is a
-weighting factor that varies between 0 and 1.  :math:`r_c` is the
+weighting factor that varies between 0 and 1.
-pairwise cutoff.  :math:`\sigma` is set equal to :math:`\sqrt{2 k_B T
-\gamma}`, where :math:`k_B` is the Boltzmann constant and *T* is the
-temperature parameter in the pair_style command.
-C is the same Coulomb conversion factor as in the pair_styles
-coul/cut and coul/long. In this way the Coulomb
-interaction between ions is corrected at small distances r, and
-the long-range interactions are computed either by the Ewald or the PPPM technique.
 
+:math:`\sigma` is set equal to :math:`\sqrt{2 k_B T \gamma}`, where
+:math:`k_B` is the Boltzmann constant and *T* is the temperature
+parameter in the pair_style command.
 
-The following parameters must be defined for each
+:math:`r_{DPD}` is the pairwise cutoff for the first 3 DPD terms in
-pair of atoms types via the :doc:`pair_coeff <pair_coeff>` command as in
+the formula as specified by *cutoff_DPD*.  For the :math:`F^E` term,
-the examples above, or in the data file or restart files read by the
+pairwise interactions within the specified *cutoff_coul* distance are
+computed directly; interactions beyond that distance are computed in
+reciprocal space.  *C* is the same Coulomb conversion factor used in
+the Coulombic formulas described on the :doc:`pair_coul <pair_coul>`
+doc page.
+
+The following parameters must be defined for each pair of atoms types
+via the :doc:`pair_coeff <pair_coeff>` command as in the examples
+above, or in the data file or restart files read by the
 :doc:`read_data <read_data>` or :doc:`read_restart <read_restart>`
 commands:
 
 * A (force units)
 * :math:`\gamma` (force/velocity units)
-* is_charged (boolean)
+* is_charged (optional boolean, default = no)
 
-
+The *is_charged* parameter is optional and can be specified as *yes* or
-.. note::
+*no*.  *Yes* should be used for interactions between two types of
-
+charged particles.  *No* is the default and should be used for
-   This style is the combination of :doc:`pair_style dpd <pair_dpd>` and :doc:`pair_style coul/slater/long <pair_coul_slater>`.
+interactions between two types of particles when one or both are
+uncharged.
 
 ----------
 
@@ -116,17 +135,17 @@ pressure.
 This pair style writes its information to :doc:`binary restart files
 <restart>`, so pair_style and pair_coeff commands do not need to be
 specified in an input script that reads a restart file.  Note that the
-user-specified random number seed is stored in the restart file, so when
+user-specified random number seed is stored in the restart file, so
-a simulation is restarted, each processor will re-initialize its random
+when a simulation is restarted, each processor will re-initialize its
-number generator the same way it did initially.  This means the random
+random number generator the same way it did initially.  This means the
-forces will be random, but will not be the same as they would have been
+random forces will be random, but will not be the same as they would
-if the original simulation had continued past the restart time.
+have been if the original simulation had continued past the restart
+time.
 
 This pair style can only be used via the *pair* keyword of the
-:doc:`run_style respa <run_style>` command.  They do not support the
+:doc:`run_style respa <run_style>` command.  It does not support the
 *inner*, *middle*, *outer* keywords.
 
-
 ----------
 
 Restrictions
@@ -138,17 +157,17 @@ LAMMPS was built with that package.  See the :doc:`Build package
 
 The default frequency for rebuilding neighbor lists is every 10 steps
 (see the :doc:`neigh_modify <neigh_modify>` command). This may be too
-infrequent since particles move rapidly and
+infrequent since particles move rapidly and can overlap by large
-can overlap by large amounts.  If this setting yields a non-zero number
+amounts.  If this setting yields a non-zero number of "dangerous"
-of "dangerous" reneighborings (printed at the end of a simulation), you
+reneighborings (printed at the end of a simulation), you should
-should experiment with forcing reneighboring more often and see if
+experiment with forcing reneighboring more often and see if system
-system energies/trajectories change.
+energies/trajectories change.
 
-This pair style requires you to use the :doc:`comm_modify vel yes
+This pair style requires use of the :doc:`comm_modify vel yes
 <comm_modify>` command so that velocities are stored by ghost atoms.
 
-This pair style also requires the long-range solvers included in the KSPACE package.
+This pair style also requires use of a long-range solvers from the
-
+KSPACE package.
 
 This pair style will not restart exactly when using the
 :doc:`read_restart <read_restart>` command, though they should provide
@@ -160,13 +179,11 @@ Related commands
 """"""""""""""""
 
 :doc:`pair_style dpd <pair_dpd>`, :doc:`pair_style coul/slater/long <pair_coul_slater>`,
-:doc:`pair_coeff <pair_coeff>`, :doc:`fix nvt <fix_nh>`, :doc:`fix langevin <fix_langevin>`,
-:doc:`pair_style srp <pair_srp>`, :doc:`fix mvv/dpd <fix_mvv_dpd>`.
 
 Default
 """""""
 
-is_charged = no
+For the pair_coeff command, the default is is_charged = no.
 
 ----------
 

doc/src/pair_pod.rst

@@ -1,8 +1,11 @@
 .. index:: pair_style pod
+.. index:: pair_style pod/kk
 
 pair_style pod command
 ========================
 
+Accelerator Variants: *pod/kk*
+
 Syntax
 """"""
 
@@ -24,29 +27,33 @@ Description
 .. versionadded:: 22Dec2022
 
 Pair style *pod* defines the proper orthogonal descriptor (POD)
-potential :ref:`(Nguyen) <Nguyen20221>`.  The mathematical definition of
+potential :ref:`(Nguyen and Rohskopf) <Nguyen20222b>`,
-the POD potential is described from :doc:`fitpod <fitpod_command>`, which is
+:ref:`(Nguyen2023) <Nguyen20232b>`, :ref:`(Nguyen2024) <Nguyen20242b>`,
-used to fit the POD potential to *ab initio* energy and force data.
+and :ref:`(Nguyen and Sema) <Nguyen20243b>`.  The :doc:`fitpod
+<fitpod_command>` is used to fit the POD potential.
 
 Only a single pair_coeff command is used with the *pod* style which
-specifies a POD parameter file followed by a coefficient file.
+specifies a POD parameter file followed by a coefficient file, a
+projection matrix file, and a centroid file.
 
-The coefficient file (``Ta_coefficients.pod``) contains coefficients for the
+The POD parameter file (``Ta_param.pod``) can contain blank and comment
-POD potential. The top of the coefficient file can contain any number of
+lines (start with #) anywhere. Each non-blank non-comment line must
-blank and comment lines (start with #), but follows a strict format
+contain one keyword/value pair. See :doc:`fitpod <fitpod_command>` for
-after that. The first non-blank non-comment line must contain:
+the description of all the keywords that can be assigned in the
+parameter file.
 
-* POD_coefficients: *ncoeff*
+The coefficient file (``Ta_coefficients.pod``) contains coefficients for
+the POD potential. The top of the coefficient file can contain any
+number of blank and comment lines (start with #), but follows a strict
+format after that. The first non-blank non-comment line must contain:
 
-This is followed by *ncoeff* coefficients, one per line. The coefficient
+* model_coefficients: *ncoeff* *nproj* *ncentroid*
+
+This is followed by *ncoeff* coefficients, *nproj* projection matrix entries,
+and *ncentroid* centroid coordinates, one per line. The coefficient
 file is generated after training the POD potential using :doc:`fitpod
 <fitpod_command>`.
 
-The POD parameter file (``Ta_param.pod``) can contain blank and comment lines
-(start with #) anywhere. Each non-blank non-comment line must contain
-one keyword/value pair. See :doc:`fitpod <fitpod_command>` for the description
-of all the keywords that can be assigned in the parameter file.
-
 As an example, if a LAMMPS indium phosphide simulation has 4 atoms
 types, with the first two being indium and the third and fourth being
 phophorous, the pair_coeff command would look like this:
@@ -67,7 +74,33 @@ the *hybrid* pair style.  The NULL values are placeholders for atom
 types that will be used with other potentials.
 
 Examples about training and using POD potentials are found in the
-directory lammps/examples/PACKAGES/pod.
+directory lammps/examples/PACKAGES/pod and the Github repo https://github.com/cesmix-mit/pod-examples.
+
+----------
+
+Mixing, shift, table, tail correction, restart, rRESPA info
+"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
+
+For atom type pairs I,J and I != J, where types I and J correspond to
+two different element types, mixing is performed by LAMMPS with
+user-specifiable parameters as described above.  You never need to
+specify a pair_coeff command with I != J arguments for this style.
+
+This pair style does not support the :doc:`pair_modify <pair_modify>`
+shift, table, and tail options.
+
+This pair style does not write its information to :doc:`binary restart
+files <restart>`, since it is stored in potential files.  Thus, you need
+to re-specify the pair_style and pair_coeff commands in an input script
+that reads a restart file.
+
+This pair style can only be used via the *pair* keyword of the
+:doc:`run_style respa <run_style>` command.  It does not support the
+*inner*, *middle*, *outer* keywords.
+
+----------
+
+.. include:: accel_styles.rst
 
 ----------
 
@@ -78,12 +111,14 @@ This style is part of the ML-POD package.  It is only enabled if LAMMPS
 was built with that package. See the :doc:`Build package
 <Build_package>` page for more info.
 
-This pair style does not compute per-atom energies and per-atom stresses.
-
 Related commands
 """"""""""""""""
 
 :doc:`fitpod <fitpod_command>`,
+:doc:`compute pod/atom <compute_pod_atom>`,
+:doc:`compute podd/atom <compute_pod_atom>`,
+:doc:`compute pod/local <compute_pod_atom>`,
+:doc:`compute pod/global <compute_pod_atom>`
 
 Default
 """""""
@@ -92,6 +127,20 @@ none
 
 ----------
 
-.. _Nguyen20221:
+.. _Nguyen20222b:
+
+**(Nguyen and Rohskopf)** Nguyen and Rohskopf,  Journal of Computational Physics, 480, 112030, (2023).
+
+.. _Nguyen20232b:
+
+**(Nguyen2023)** Nguyen, Physical Review B, 107(14), 144103, (2023).
+
+.. _Nguyen20242b:
+
+**(Nguyen2024)** Nguyen, Journal of Computational Physics, 113102, (2024).
+
+.. _Nguyen20243b:
+
+**(Nguyen and Sema)** Nguyen and Sema, https://arxiv.org/abs/2405.00306, (2024).
+
 
-**(Nguyen)** Nguyen and Rohskopf, arXiv preprint arXiv:2209.02362 (2022).

doc/src/pair_uf3.rst

@@ -36,7 +36,7 @@ Examples
 Description
 """""""""""
 
-.. versionadded:: TBD
+.. versionadded:: 27June2024
 
 The *uf3* style computes the :ref:`Ultra-Fast Force Fields (UF3)
 <Xie23>` potential, a machine-learning interatomic potential. In UF3,

doc/src/variable.rst

@@ -67,7 +67,7 @@ Syntax
                            bound(group,dir,region), gyration(group,region), ke(group,reigon),
                            angmom(group,dim,region), torque(group,dim,region),
                            inertia(group,dimdim,region), omega(group,dim,region)
-         special functions = sum(x), min(x), max(x), ave(x), trap(x), slope(x), sort(x), rsort(x), gmask(x), rmask(x), grmask(x,y), next(x), is_file(name), is_os(name), extract_setting(name), label2type(kind,label), is_typelabel(kind,label)
+         special functions = sum(x), min(x), max(x), ave(x), trap(x), slope(x), sort(x), rsort(x), gmask(x), rmask(x), grmask(x,y), next(x), is_file(name), is_os(name), extract_setting(name), label2type(kind,label), is_typelabel(kind,label), is_timeout()
          feature functions = is_available(category,feature), is_active(category,feature), is_defined(category,id)
          atom value = id[i], mass[i], type[i], mol[i], x[i], y[i], z[i], vx[i], vy[i], vz[i], fx[i], fy[i], fz[i], q[i]
          atom vector = id, mass, type, mol, radius, q, x, y, z, vx, vy, vz, fx, fy, fz
@@ -547,7 +547,7 @@ variables.
 +------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
 | Region functions       | count(ID,IDR), mass(ID,IDR), charge(ID,IDR), xcm(ID,dim,IDR), vcm(ID,dim,IDR), fcm(ID,dim,IDR), bound(ID,dir,IDR), gyration(ID,IDR), ke(ID,IDR), angmom(ID,dim,IDR), torque(ID,dim,IDR), inertia(ID,dimdim,IDR), omega(ID,dim,IDR)                                                                                                                |
 +------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
-| Special functions      | sum(x), min(x), max(x), ave(x), trap(x), slope(x), sort(x), rsort(x), gmask(x), rmask(x), grmask(x,y), next(x), is_file(name), is_os(name), extract_setting(name), label2type(kind,label), is_typelabel(kind,label)                                                                                                                               |
+| Special functions      | sum(x), min(x), max(x), ave(x), trap(x), slope(x), sort(x), rsort(x), gmask(x), rmask(x), grmask(x,y), next(x), is_file(name), is_os(name), extract_setting(name), label2type(kind,label), is_typelabel(kind,label), is_timeout()                                                                                                                 |
 +------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
 | Feature functions      | is_available(category,feature), is_active(category,feature), is_defined(category,id)                                                                                                                                                                                                                                                              |
 +------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
@@ -957,7 +957,7 @@ of points, equally spaced by 1 in their x coordinate: (1,V1), (2,V2),
 length N.  The returned value is the slope of the line.  If the line
 has a single point or is vertical, it returns 1.0e20.
 
-.. versionadded:: TBD
+.. versionadded:: 27June2024
 
 The sort(x) and rsort(x) functions sort the data of the input vector by
 their numeric value: sort(x) sorts in ascending order, rsort(x) sorts
@@ -1042,6 +1042,20 @@ label2type(), but returns 1 if the type label has been assigned,
 otherwise it returns 0.  This function can be used to check if a
 particular type label already exists in the simulation.
 
+.. versionadded:: TBD
+
+The is_timeout() function returns 1 when the :doc:`timer timeout
+<timer>` has expired otherwise it returns 0.  This function can be used
+to check inputs in combination with the :doc:`if command <if>` to
+execute commands after the timer has expired. Example:
+
+.. code-block:: LAMMPS
+
+   variable timeout equal is_timeout()
+   timer timeout 0:10:00 every 10
+   run 10000
+   if ${timeout} then "print 'Timer has expired'"
+
 ----------
 
 Feature Functions

doc/utils/requirements.txt

@@ -1,6 +1,7 @@
 Sphinx >= 5.3.0, <8.0
 sphinxcontrib-spelling
 sphinxcontrib-jquery
+sphinx-design
 git+https://github.com/akohlmey/sphinx-fortran@parallel-read
 sphinx-tabs>=3.4.1
 breathe

doc/utils/sphinx-config/conf.py.in

@@ -57,6 +57,7 @@ extensions = [
     'table_from_list',
     'tab_or_note',
     'breathe',
+    'sphinx_design'
 ]
 
 images_config = {

doc/utils/sphinx-config/false_positives.txt

@@ -1173,6 +1173,7 @@ finitecutflag
 Finnis
 Fiorin
 fitpod
+fivebody
 fixID
 fj
 Fji
@@ -2897,6 +2898,7 @@ Pmolrotate
 Pmoltrans
 pN
 png
+podd
 Podhorszki
 Poiseuille
 poisson
@@ -3370,6 +3372,7 @@ setmask
 Setmask
 setpoint
 setvel
+sevenbody
 sfftw
 sfree
 Sg
@@ -3420,6 +3423,7 @@ SiO
 Siochi
 Sirk
 Sival
+sixbody
 sizeI
 sizeJ
 sizex
@@ -3735,7 +3739,6 @@ tokyo
 tol
 tomic
 toolchain
-toolset
 topologies
 Toporov
 Torder
@@ -3813,6 +3816,7 @@ typeJ
 typelabel
 typeN
 typesafe
+typestr
 Tz
 Tzou
 ub

examples/PACKAGES/pod/InP/InP_coefficients.pod

@@ -0,0 +1,305 @@
+model_coefficients: 304 0 0
+-3.756301 
+914.674801
+-370.747265
+-141.227291
+97.101196 
+-59.216907
+9.975284  
+87.329406 
+-10.969150
+14.411744 
+-2.270453 
+0.798817  
+-0.121719 
+114.805574
+-2631.563672
+-869.027988
+-1038.286258
+2431.480027
+31.972558 
+139.437898
+29.230520 
+39.179879 
+-189.998549
+-16.358691
+18.699184 
+13.386293 
+12.847911 
+7.310155  
+1.677341  
+-9.237073 
+-2.228285 
+0.137303  
+6.446888  
+-0.385837 
+0.272000  
+0.111052  
+-1.264342 
+-0.711451 
+450.463638
+-499.339551
+550.704146
+-1638.278950
+-1311.408792
+-24.811632
+-14.000684
+-39.928838
+44.690659 
+35.934791 
+-0.425535 
+16.810067 
+-1.951262 
+26.118670 
+28.549237 
+-1.779991 
+-1.907896 
+4.278671  
+-5.852529 
+-11.518503
+0.285252  
+0.210939  
+-1.153276 
+0.744801  
+2.765281  
+-365.425648
+892.154409
+616.198109
+-808.930752
+-241.494545
+60.329248 
+-50.220263
+-89.366098
+47.692144 
+12.376825 
+-11.304060
+-0.465577 
+20.908593 
+0.768057  
+-0.296966 
+-1.434787 
+0.089423  
+-3.273582 
+1.085951  
+1.627005  
+0.063449  
+0.501713  
+-0.025247 
+-1.127277 
+-0.619276 
+-950.742997
+11175.508296
+1041.077100
+-8713.542159
+11.024588 
+-193.368092
+-17.871650
+193.000879
+-1.221800 
+0.201038  
+-0.297456 
+10.197177 
+0.118306  
+-2.486775 
+0.340362  
+0.179573  
+2064.315112
+11898.567992
+-7130.614814
+-2965.017905
+-36.665484
+-156.646217
+112.838247
+64.147104 
+-0.187677 
+8.822337  
+-2.516814 
+0.833110  
+-0.808597 
+-3.112898 
+2.172317  
+1.684634  
+-5.757502 
+4129.051881
+-2191.420379
+-5640.863432
+2.123836  
+-34.024960
+35.525113 
+106.884920
+0.406772  
+6.365527  
+-0.015093 
+2.711538  
+-0.263692 
+-0.604293 
+0.790243  
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+-2785.368577
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+4424.744171
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+-0.114050 
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+28.153323 
+-15.183264
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+1133.815010
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+-267.931116
+-631.685867
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+-104.334909
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+-1.835511 
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+-0.881517 
+-0.703873 
+0.712785  
+-567.114384
+363.884433
+-300.309621
+-1421.591050
+-1083.371637
+45.559123 
+-7.797512 
+24.330267 
+71.829748 
+60.799510 
+-2.099976 
+-9.821055 
+-6.488823 
+9.426431  
+6.385231  
+-0.836215 
+3.533300  
+2.741734  
+-3.602311 
+-3.863372 
+-0.122980 
+-0.147120 
+-0.378902 
+-0.232987 
+0.445875  
+-237.448044
+442.663085
+2103.157345
+-2382.920549
+0.583996  
+-6.353184 
+-17.798247
+72.320744 
+-0.422216 
+1.198193  
+3.257409  
+6.944903  
+0.255190  
+-0.887514 
+-0.316214 
+0.345565  
+-242.443134
+4329.522091
+534.487792
+-4571.367114
+-9.591790 
+-62.990215
+20.323544 
+169.640829
+-2.788146 
+2.114659  
+7.272737  
+21.210166 
+0.904969  
+-1.154060 
+-1.376235 
+-1.148246 
+129.689234
+5953.209838
+667.823321
+-83.797221
+3.417016  
+-126.968016
+-14.909772
+41.785404 
+1.415997  
+-5.278588 
+-0.463605 
+8.009232  
+0.030211  
+-0.765006 
+-0.826223 
+0.103515  
+147.565462
+4404.556538
+3774.833555
+-2327.923578
+-5.422196 
+-107.433002
+-70.175719
+74.887031 
+-0.424490 
+-6.620110 
+-2.179770 
+5.588150  
+-0.222514 
+-0.435209 
+0.034179  
+0.388588  

examples/PACKAGES/pod/InP/InP_data.pod

@@ -1,20 +1,21 @@
 file_format extxyz
 file_extension xyz
 
-path_to_training_data_set "../Ta/XYZ"
+path_to_training_data_set "XYZ"
-path_to_test_data_set "../Ta/XYZ"
+path_to_test_data_set "XYZ"
+path_to_environment_configuration_set "XYZ"
 
 fitting_weight_energy 100.0
 fitting_weight_force 1.0
-fitting_regularization_parameter 1e-10
+fitting_regularization_parameter 1e-12
 
 error_analysis_for_training_data_set 1
 error_analysis_for_test_data_set 0
 
 # Add the following basename to the name of output files
-basename_for_output_files Ta
+basename_for_output_files InP
 
 # number of digits after the decimal point for pod coefficients
-precision_for_pod_coefficients 5
+precision_for_pod_coefficients 6
 
 

examples/PACKAGES/pod/InP/InP_param.pod

@@ -0,0 +1,48 @@
+# chemical element symbols
+species In P
+
+# periodic boundary conditions
+pbc 1 1 1
+
+# inner cut-off radius
+rin 0.8
+
+# outer cut-off radius
+rcut 5.0
+
+# use only for enviroment-adaptive potentials
+number_of_environment_clusters 1
+
+# principal_components of local descriptors
+number_of_principal_components 2
+
+# polynomial degrees for radial basis functions
+bessel_polynomial_degree 4
+inverse_polynomial_degree 8
+
+# one-body potential
+onebody 1
+
+# two-body linear POD potential
+twobody_number_radial_basis_functions 6
+
+# three-body linear POD potential
+threebody_number_radial_basis_functions 5
+threebody_angular_degree 4
+
+# four-body linear POD potential
+fourbody_number_radial_basis_functions 4
+fourbody_angular_degree 2
+
+# five-body linear POD potential
+fivebody_number_radial_basis_functions 0
+fivebody_angular_degree 0
+
+# six-body linear POD potential
+sixbody_number_radial_basis_functions 0
+sixbody_angular_degree 0
+
+# seven-body linear POD potential
+sevenbody_number_radial_basis_functions 0
+sevenbody_angular_degree 0
+

examples/PACKAGES/pod/InP/InP_training_errors.pod

@@ -0,0 +1,27 @@
+**************** Begin of Error Analysis for the Training Data Set ****************
+--------------------------------------------------------------------------------------------
+     File     | # configs |  # atoms  | MAE energy  | RMSE energy | MAE force  | RMSE force
+--------------------------------------------------------------------------------------------
+Bulk.xyz              1           8     0.001678      0.001678      0.000000      0.000000  
+EOS.xyz             268        2080     0.001463      0.001817      0.001107      0.015463  
+Shear.xyz           346        2768     0.000415      0.000640      0.008336      0.012865  
+Strain.xyz          163        1304     0.001129      0.001374      0.000021      0.000036  
+aIn.xyz              54       11664     0.000737      0.000796      0.007969      0.016112  
+aP.xyz               21        4536     0.001396      0.001407      0.019599      0.054174  
+aa.xyz               20        4320     0.001991      0.001991      0.016735      0.027955  
+iIn.xyz              41        8897     0.001548      0.001687      0.013910      0.025462  
+iP.xyz              100       21700     0.001090      0.001203      0.009692      0.018549  
+s_aIn.xyz           121        7744     0.000856      0.000889      0.011041      0.017399  
+s_aP.xyz             72        4608     0.002255      0.003587      0.032425      0.045878  
+s_aa.xyz             18        1152     0.001198      0.001200      0.037169      0.047713  
+s_iIn.xyz           144        9360     0.002014      0.002255      0.035374      0.050726  
+s_iP.xyz            337       21905     0.001655      0.002178      0.025130      0.038368  
+s_vIn.xyz            17        1071     0.007984      0.007992      0.023190      0.039575  
+s_vP.xyz             77        4851     0.000245      0.000281      0.018303      0.025819  
+s_vv.xyz             65        4030     0.001759      0.001986      0.039037      0.052667  
+vP.xyz               10        2150     0.000640      0.000640      0.005452      0.009834  
+vv.xyz               19        4066     0.001336      0.001403      0.020930      0.034386  
+--------------------------------------------------------------------------------------------
+All files          1894      118214     0.001288      0.001855      0.018109      0.032649  
+--------------------------------------------------------------------------------------------
+**************** End of Error Analysis for the Training Data Set ****************

examples/PACKAGES/pod/InP/README.md

@@ -0,0 +1,16 @@
+### POD example for InP
+
+We will fit a potential to the `InP` training data in the `XYZ` directory, which houses `.xyz` files 
+
+Please download the training data from [the repo](https://github.com/cesmix-mit/pod-examples/tree/main/JCP2023_InP/XYZ)
+
+Fit POD with
+
+    lmp -in in.fitpod
+
+This creates `InP_coefficients.pod` for the linear model, which we can use to run MD with
+
+    lmp -in in.pod
+
+
+ 

examples/PACKAGES/pod/InP/in.fitpod

@@ -0,0 +1 @@
+fitpod InP_param.pod InP_data.pod

examples/PACKAGES/pod/InP/in.pod

@@ -1,13 +1,13 @@
-# Demonstrate POD Ta potential
+# Demonstrate POD potential for InP 
 
 # Initialize simulation
 
 variable nsteps index 100
 variable nrep equal 4
-variable a equal 3.316
+variable a equal 5.83
 units           metal
 
-# generate the box and atom positions using a BCC lattice
+# generate the box and atom positions using a FCC lattice
 
 variable nx equal ${nrep}
 variable ny equal ${nrep}
@@ -15,17 +15,17 @@ variable nz equal ${nrep}
 
 boundary        p p p
 
-lattice         bcc $a
+lattice         diamond $a
 region          box block 0 ${nx} 0 ${ny} 0 ${nz}
-create_box      1 box
+create_box      2 box
-create_atoms    1 box
+create_atoms    1 box basis 5 2 basis 6 2 basis 7 2 basis 8 2
-
-mass 1 180.88
 
+mass 1 114.76
+mass 2 30.98
 
 # POD potential
 pair_style pod
-pair_coeff * * Ta_param.pod Ta_coefficients.pod Ta
+pair_coeff * * InP_param.pod InP_coefficients.pod In P
 
 # Setup output
 
@@ -44,4 +44,3 @@ velocity all create 300.0 4928459 loop geom
 fix 1 all nve
 run             ${nsteps}
 
-

examples/PACKAGES/pod/InP/log.22May24.fitpod.g++.1

@@ -0,0 +1,163 @@
+LAMMPS (17 Apr 2024 - Development - patch_17Apr2024-176-gc2e4ad220f-modified)
+OMP_NUM_THREADS environment is not set. Defaulting to 1 thread. (src/comm.cpp:98)
+  using 1 OpenMP thread(s) per MPI task
+fitpod InP_param.pod InP_data.pod
+**************** Begin of POD Potentials ****************
+species: In P 
+periodic boundary conditions: 1 1 1
+number of environment clusters: 1
+number of principal compoments: 2
+inner cut-off radius: 0.8
+outer cut-off radius: 5
+bessel polynomial degree: 4
+inverse polynomial degree: 8
+one-body potential: 1
+two-body radial basis functions: 6
+three-body radial basis functions: 5
+three-body angular degree: 4
+four-body radial basis functions: 4
+four-body angular degree: 2
+five-body radial basis functions: 0
+five-body angular degree: 0
+six-body radial basis functions: 0
+six-body angular degree: 0
+seven-body radial basis functions: 0
+seven-body angular degree: 0
+number of local descriptors per element for one-body potential: 1
+number of local descriptors per element for two-body potential: 12
+number of local descriptors per element for three-body potential: 75
+number of local descriptors per element for four-body potential: 64
+number of local descriptors per element for five-body potential: 0
+number of local descriptors per element for six-body potential: 0
+number of local descriptors per element for seven-body potential: 0
+number of local descriptors per element for all potentials: 152
+number of global descriptors: 304
+**************** End of POD Potentials ****************
+
+**************** Begin of Data File ****************
+file format: extxyz
+file extension: xyz
+path to training data set: XYZ
+path to test data set: XYZ
+path to environment configuration set: XYZ
+basename for output files: InP
+training fraction: 1
+test fraction: 1
+randomize training data set: 1
+randomize test data set: 1
+error analysis for training data set: 1
+error analysis for test data set: 0
+energy/force calculation for training data set: 0
+energy/force calculation for test data set: 0
+fitting weight for energy: 100
+fitting weight for force: 1
+fitting weight for stress: 0
+save pod descriptors: 0
+compute pod descriptors: 0
+**************** End of Data File ****************
+**************** Begin of Training Data Set ****************
+--------------------------------------------------------
+ data file  | number of configurations | number of atoms
+--------------------------------------------------------
+ Bulk.xyz   |                 1        |           8
+ EOS.xyz    |               268        |        2080
+ Shear.xyz  |               346        |        2768
+ Strain.xyz |               163        |        1304
+ aIn.xyz    |                54        |       11664
+ aP.xyz     |                21        |        4536
+ aa.xyz     |                20        |        4320
+ iIn.xyz    |                41        |        8897
+ iP.xyz     |               100        |       21700
+ s_aIn.xyz  |               121        |        7744
+ s_aP.xyz   |                72        |        4608
+ s_aa.xyz   |                18        |        1152
+ s_iIn.xyz  |               144        |        9360
+ s_iP.xyz   |               337        |       21905
+ s_vIn.xyz  |                17        |        1071
+ s_vP.xyz   |                77        |        4851
+ s_vv.xyz   |                65        |        4030
+ vP.xyz     |                10        |        2150
+ vv.xyz     |                19        |        4066
+--------------------------------------------------------
+number of files: 19
+number of configurations in all files: 1894
+number of atoms in all files: 118214
+minimum number of atoms: 4
+maximum number of atoms: 217
+**************** End of Training Data Set ****************
+**************** Begin of Memory Allocation ****************
+maximum number of atoms in periodic domain: 217
+maximum number of atoms in extended domain: 5859
+maximum number of neighbors in extended domain: 1271403
+size of double memory: 5555904
+size of descriptor matrix: 304 x 304
+**************** End of Memory Allocation ****************
+**************** Begin of Least-Squares Fitting ****************
+Configuration: # 1
+Configuration: # 101
+Configuration: # 201
+Configuration: # 301
+Configuration: # 401
+Configuration: # 501
+Configuration: # 601
+Configuration: # 701
+Configuration: # 801
+Configuration: # 901
+Configuration: # 1001
+Configuration: # 1101
+Configuration: # 1201
+Configuration: # 1301
+Configuration: # 1401
+Configuration: # 1501
+Configuration: # 1601
+Configuration: # 1701
+Configuration: # 1801
+**************** Begin of Error Calculation ****************
+Configuration: # 1
+Configuration: # 101
+Configuration: # 201
+Configuration: # 301
+Configuration: # 401
+Configuration: # 501
+Configuration: # 601
+Configuration: # 701
+Configuration: # 801
+Configuration: # 901
+Configuration: # 1001
+Configuration: # 1101
+Configuration: # 1201
+Configuration: # 1301
+Configuration: # 1401
+Configuration: # 1501
+Configuration: # 1601
+Configuration: # 1701
+Configuration: # 1801
+**************** End of Error Calculation ****************
+**************** Begin of Error Analysis for the Training Data Set ****************
+--------------------------------------------------------------------------------------------
+     File     | # configs |  # atoms  | MAE energy  | RMSE energy | MAE force  | RMSE force
+--------------------------------------------------------------------------------------------
+Bulk.xyz              1           8     0.001678      0.001678      0.000000      0.000000  
+EOS.xyz             268        2080     0.001463      0.001817      0.001107      0.015464  
+Shear.xyz           346        2768     0.000415      0.000640      0.008335      0.012863  
+Strain.xyz          163        1304     0.001129      0.001374      0.000021      0.000036  
+aIn.xyz              54       11664     0.000737      0.000796      0.007969      0.016112  
+aP.xyz               21        4536     0.001396      0.001407      0.019599      0.054174  
+aa.xyz               20        4320     0.001991      0.001991      0.016735      0.027955  
+iIn.xyz              41        8897     0.001548      0.001687      0.013910      0.025462  
+iP.xyz              100       21700     0.001090      0.001203      0.009692      0.018549  
+s_aIn.xyz           121        7744     0.000856      0.000889      0.011041      0.017399  
+s_aP.xyz             72        4608     0.002255      0.003587      0.032425      0.045878  
+s_aa.xyz             18        1152     0.001198      0.001200      0.037169      0.047713  
+s_iIn.xyz           144        9360     0.002014      0.002255      0.035374      0.050726  
+s_iP.xyz            337       21905     0.001655      0.002178      0.025130      0.038368  
+s_vIn.xyz            17        1071     0.007984      0.007992      0.023190      0.039575  
+s_vP.xyz             77        4851     0.000245      0.000281      0.018303      0.025818  
+s_vv.xyz             65        4030     0.001759      0.001986      0.039037      0.052667  
+vP.xyz               10        2150     0.000640      0.000640      0.005452      0.009834  
+vv.xyz               19        4066     0.001336      0.001403      0.020930      0.034386  
+--------------------------------------------------------------------------------------------
+All files          1894      118214     0.001288      0.001855      0.018109      0.032648  
+--------------------------------------------------------------------------------------------
+**************** End of Error Analysis for the Training Data Set ****************
+Total wall time: 0:00:27

examples/PACKAGES/pod/InP/log.22May24.fitpod.g++.4

@@ -0,0 +1,163 @@
+LAMMPS (17 Apr 2024 - Development - patch_17Apr2024-176-gc2e4ad220f-modified)
+OMP_NUM_THREADS environment is not set. Defaulting to 1 thread. (src/comm.cpp:98)
+  using 1 OpenMP thread(s) per MPI task
+fitpod InP_param.pod InP_data.pod
+**************** Begin of POD Potentials ****************
+species: In P 
+periodic boundary conditions: 1 1 1
+number of environment clusters: 1
+number of principal compoments: 2
+inner cut-off radius: 0.8
+outer cut-off radius: 5
+bessel polynomial degree: 4
+inverse polynomial degree: 8
+one-body potential: 1
+two-body radial basis functions: 6
+three-body radial basis functions: 5
+three-body angular degree: 4
+four-body radial basis functions: 4
+four-body angular degree: 2
+five-body radial basis functions: 0
+five-body angular degree: 0
+six-body radial basis functions: 0
+six-body angular degree: 0
+seven-body radial basis functions: 0
+seven-body angular degree: 0
+number of local descriptors per element for one-body potential: 1
+number of local descriptors per element for two-body potential: 12
+number of local descriptors per element for three-body potential: 75
+number of local descriptors per element for four-body potential: 64
+number of local descriptors per element for five-body potential: 0
+number of local descriptors per element for six-body potential: 0
+number of local descriptors per element for seven-body potential: 0
+number of local descriptors per element for all potentials: 152
+number of global descriptors: 304
+**************** End of POD Potentials ****************
+
+**************** Begin of Data File ****************
+file format: extxyz
+file extension: xyz
+path to training data set: XYZ
+path to test data set: XYZ
+path to environment configuration set: XYZ
+basename for output files: InP
+training fraction: 1
+test fraction: 1
+randomize training data set: 1
+randomize test data set: 1
+error analysis for training data set: 1
+error analysis for test data set: 0
+energy/force calculation for training data set: 0
+energy/force calculation for test data set: 0
+fitting weight for energy: 100
+fitting weight for force: 1
+fitting weight for stress: 0
+save pod descriptors: 0
+compute pod descriptors: 0
+**************** End of Data File ****************
+**************** Begin of Training Data Set ****************
+--------------------------------------------------------
+ data file  | number of configurations | number of atoms
+--------------------------------------------------------
+ Bulk.xyz   |                 1        |           8
+ EOS.xyz    |               268        |        2080
+ Shear.xyz  |               346        |        2768
+ Strain.xyz |               163        |        1304
+ aIn.xyz    |                54        |       11664
+ aP.xyz     |                21        |        4536
+ aa.xyz     |                20        |        4320
+ iIn.xyz    |                41        |        8897
+ iP.xyz     |               100        |       21700
+ s_aIn.xyz  |               121        |        7744
+ s_aP.xyz   |                72        |        4608
+ s_aa.xyz   |                18        |        1152
+ s_iIn.xyz  |               144        |        9360
+ s_iP.xyz   |               337        |       21905
+ s_vIn.xyz  |                17        |        1071
+ s_vP.xyz   |                77        |        4851
+ s_vv.xyz   |                65        |        4030
+ vP.xyz     |                10        |        2150
+ vv.xyz     |                19        |        4066
+--------------------------------------------------------
+number of files: 19
+number of configurations in all files: 1894
+number of atoms in all files: 118214
+minimum number of atoms: 4
+maximum number of atoms: 217
+**************** End of Training Data Set ****************
+**************** Begin of Memory Allocation ****************
+maximum number of atoms in periodic domain: 217
+maximum number of atoms in extended domain: 5859
+maximum number of neighbors in extended domain: 1271403
+size of double memory: 5555904
+size of descriptor matrix: 304 x 304
+**************** End of Memory Allocation ****************
+**************** Begin of Least-Squares Fitting ****************
+Configuration: # 1
+Configuration: # 101
+Configuration: # 201
+Configuration: # 301
+Configuration: # 401
+Configuration: # 501
+Configuration: # 601
+Configuration: # 701
+Configuration: # 801
+Configuration: # 901
+Configuration: # 1001
+Configuration: # 1101
+Configuration: # 1201
+Configuration: # 1301
+Configuration: # 1401
+Configuration: # 1501
+Configuration: # 1601
+Configuration: # 1701
+Configuration: # 1801
+**************** Begin of Error Calculation ****************
+Configuration: # 1
+Configuration: # 101
+Configuration: # 201
+Configuration: # 301
+Configuration: # 401
+Configuration: # 501
+Configuration: # 601
+Configuration: # 701
+Configuration: # 801
+Configuration: # 901
+Configuration: # 1001
+Configuration: # 1101
+Configuration: # 1201
+Configuration: # 1301
+Configuration: # 1401
+Configuration: # 1501
+Configuration: # 1601
+Configuration: # 1701
+Configuration: # 1801
+**************** End of Error Calculation ****************
+**************** Begin of Error Analysis for the Training Data Set ****************
+--------------------------------------------------------------------------------------------
+     File     | # configs |  # atoms  | MAE energy  | RMSE energy | MAE force  | RMSE force
+--------------------------------------------------------------------------------------------
+Bulk.xyz              1           8     0.001678      0.001678      0.000000      0.000000  
+EOS.xyz             268        2080     0.001463      0.001817      0.001107      0.015463  
+Shear.xyz           346        2768     0.000415      0.000640      0.008336      0.012865  
+Strain.xyz          163        1304     0.001129      0.001374      0.000021      0.000036  
+aIn.xyz              54       11664     0.000737      0.000796      0.007969      0.016112  
+aP.xyz               21        4536     0.001396      0.001407      0.019599      0.054174  
+aa.xyz               20        4320     0.001991      0.001991      0.016735      0.027955  
+iIn.xyz              41        8897     0.001548      0.001687      0.013910      0.025462  
+iP.xyz              100       21700     0.001090      0.001203      0.009692      0.018549  
+s_aIn.xyz           121        7744     0.000856      0.000889      0.011041      0.017399  
+s_aP.xyz             72        4608     0.002255      0.003587      0.032425      0.045878  
+s_aa.xyz             18        1152     0.001198      0.001200      0.037169      0.047713  
+s_iIn.xyz           144        9360     0.002014      0.002255      0.035374      0.050726  
+s_iP.xyz            337       21905     0.001655      0.002178      0.025130      0.038368  
+s_vIn.xyz            17        1071     0.007984      0.007992      0.023190      0.039575  
+s_vP.xyz             77        4851     0.000245      0.000281      0.018303      0.025819  
+s_vv.xyz             65        4030     0.001759      0.001986      0.039037      0.052667  
+vP.xyz               10        2150     0.000640      0.000640      0.005452      0.009834  
+vv.xyz               19        4066     0.001336      0.001403      0.020930      0.034386  
+--------------------------------------------------------------------------------------------
+All files          1894      118214     0.001288      0.001855      0.018109      0.032649  
+--------------------------------------------------------------------------------------------
+**************** End of Error Analysis for the Training Data Set ****************
+Total wall time: 0:00:10

examples/PACKAGES/pod/InP/log.22May24.pod.g++.1

@@ -0,0 +1,155 @@
+LAMMPS (17 Apr 2024 - Development - patch_17Apr2024-176-gc2e4ad220f-modified)
+OMP_NUM_THREADS environment is not set. Defaulting to 1 thread. (src/comm.cpp:98)
+  using 1 OpenMP thread(s) per MPI task
+# Demonstrate POD potential for InP
+
+# Initialize simulation
+
+variable nsteps index 100
+variable nrep equal 4
+variable a equal 5.83
+units           metal
+
+# generate the box and atom positions using a FCC lattice
+
+variable nx equal ${nrep}
+variable nx equal 4
+variable ny equal ${nrep}
+variable ny equal 4
+variable nz equal ${nrep}
+variable nz equal 4
+
+boundary        p p p
+
+lattice         diamond $a
+lattice         diamond 5.83
+Lattice spacing in x,y,z = 5.83 5.83 5.83
+region          box block 0 ${nx} 0 ${ny} 0 ${nz}
+region          box block 0 4 0 ${ny} 0 ${nz}
+region          box block 0 4 0 4 0 ${nz}
+region          box block 0 4 0 4 0 4
+create_box      2 box
+Created orthogonal box = (0 0 0) to (23.32 23.32 23.32)
+  1 by 1 by 1 MPI processor grid
+create_atoms    1 box basis 5 2 basis 6 2 basis 7 2 basis 8 2
+Created 512 atoms
+  using lattice units in orthogonal box = (0 0 0) to (23.32 23.32 23.32)
+  create_atoms CPU = 0.001 seconds
+
+mass 1 114.76
+mass 2 30.98
+
+# POD potential
+pair_style pod
+pair_coeff * * InP_param.pod InP_coefficients.pod In P
+**************** Begin of POD Potentials ****************
+species: In P 
+periodic boundary conditions: 1 1 1
+number of environment clusters: 1
+number of principal compoments: 2
+inner cut-off radius: 0.8
+outer cut-off radius: 5
+bessel polynomial degree: 4
+inverse polynomial degree: 8
+one-body potential: 1
+two-body radial basis functions: 6
+three-body radial basis functions: 5
+three-body angular degree: 4
+four-body radial basis functions: 4
+four-body angular degree: 2
+five-body radial basis functions: 0
+five-body angular degree: 0
+six-body radial basis functions: 0
+six-body angular degree: 0
+seven-body radial basis functions: 0
+seven-body angular degree: 0
+number of local descriptors per element for one-body potential: 1
+number of local descriptors per element for two-body potential: 12
+number of local descriptors per element for three-body potential: 75
+number of local descriptors per element for four-body potential: 64
+number of local descriptors per element for five-body potential: 0
+number of local descriptors per element for six-body potential: 0
+number of local descriptors per element for seven-body potential: 0
+number of local descriptors per element for all potentials: 152
+number of global descriptors: 304
+**************** End of POD Potentials ****************
+
+**************** Begin of Model Coefficients ****************
+total number of coefficients for POD potential: 304
+total number of elements for PCA projection matrix: 0
+total number of elements for PCA centroids: 0
+**************** End of Model Coefficients ****************
+
+
+# Setup output
+
+thermo          10
+thermo_modify norm yes
+
+# Set up NVE run
+
+timestep 0.5e-3
+neighbor 1.0 bin
+neigh_modify once no every 1 delay 0 check yes
+
+# Run MD
+
+velocity all create 300.0 4928459 loop geom
+fix 1 all nve
+run             ${nsteps}
+run             100
+Neighbor list info ...
+  update: every = 1 steps, delay = 0 steps, check = yes
+  max neighbors/atom: 2000, page size: 100000
+  master list distance cutoff = 6
+  ghost atom cutoff = 6
+  binsize = 3, bins = 8 8 8
+  1 neighbor lists, perpetual/occasional/extra = 1 0 0
+  (1) pair pod, perpetual
+      attributes: full, newton on
+      pair build: full/bin/atomonly
+      stencil: full/bin/3d
+      bin: standard
+Per MPI rank memory allocation (min/avg/max) = 3.244 | 3.244 | 3.244 Mbytes
+   Step          Temp          E_pair         E_mol          TotEng         Press     
+         0   300           -4.8392777      0             -4.8005754      1561.0654    
+        10   291.27079     -4.8381515      0             -4.8005753      1709.509     
+        20   266.69372     -4.8349805      0             -4.8005749      2126.86      
+        30   230.86163     -4.8303573      0             -4.8005744      2735.6894    
+        40   190.64668     -4.8251686      0             -4.8005738      3416.9247    
+        50   153.9516      -4.8204341      0             -4.8005732      4022.2533    
+        60   127.93805     -4.8170778      0             -4.8005728      4405.9763    
+        70   117.12501     -4.8156828      0             -4.8005727      4475.6131    
+        80   122.09497     -4.8163242      0             -4.800573       4231.7934    
+        90   139.42686     -4.8185607      0             -4.8005735      3766.8505    
+       100   162.84813     -4.8215828      0             -4.8005741      3221.8605    
+Loop time of 2.18542 on 1 procs for 100 steps with 512 atoms
+
+Performance: 1.977 ns/day, 12.141 hours/ns, 45.758 timesteps/s, 23.428 katom-step/s
+97.9% CPU use with 1 MPI tasks x 1 OpenMP threads
+
+MPI task timing breakdown:
+Section |  min time  |  avg time  |  max time  |%varavg| %total
+---------------------------------------------------------------
+Pair    | 2.1829     | 2.1829     | 2.1829     |   0.0 | 99.88
+Neigh   | 0          | 0          | 0          |   0.0 |  0.00
+Comm    | 0.00080748 | 0.00080748 | 0.00080748 |   0.0 |  0.04
+Output  | 0.00033584 | 0.00033584 | 0.00033584 |   0.0 |  0.02
+Modify  | 0.00071224 | 0.00071224 | 0.00071224 |   0.0 |  0.03
+Other   |            | 0.000686   |            |       |  0.03
+
+Nlocal:            512 ave         512 max         512 min
+Histogram: 1 0 0 0 0 0 0 0 0 0
+Nghost:           1451 ave        1451 max        1451 min
+Histogram: 1 0 0 0 0 0 0 0 0 0
+Neighs:              0 ave           0 max           0 min
+Histogram: 1 0 0 0 0 0 0 0 0 0
+FullNghs:        17408 ave       17408 max       17408 min
+Histogram: 1 0 0 0 0 0 0 0 0 0
+
+Total # of neighbors = 17408
+Ave neighs/atom = 34
+Neighbor list builds = 0
+Dangerous builds = 0
+
+Total wall time: 0:00:02

examples/PACKAGES/pod/InP/log.22May24.pod.g++.4

@@ -0,0 +1,155 @@
+LAMMPS (17 Apr 2024 - Development - patch_17Apr2024-176-gc2e4ad220f-modified)
+OMP_NUM_THREADS environment is not set. Defaulting to 1 thread. (src/comm.cpp:98)
+  using 1 OpenMP thread(s) per MPI task
+# Demonstrate POD potential for InP
+
+# Initialize simulation
+
+variable nsteps index 100
+variable nrep equal 4
+variable a equal 5.83
+units           metal
+
+# generate the box and atom positions using a FCC lattice
+
+variable nx equal ${nrep}
+variable nx equal 4
+variable ny equal ${nrep}
+variable ny equal 4
+variable nz equal ${nrep}
+variable nz equal 4
+
+boundary        p p p
+
+lattice         diamond $a
+lattice         diamond 5.83
+Lattice spacing in x,y,z = 5.83 5.83 5.83
+region          box block 0 ${nx} 0 ${ny} 0 ${nz}
+region          box block 0 4 0 ${ny} 0 ${nz}
+region          box block 0 4 0 4 0 ${nz}
+region          box block 0 4 0 4 0 4
+create_box      2 box
+Created orthogonal box = (0 0 0) to (23.32 23.32 23.32)
+  1 by 2 by 2 MPI processor grid
+create_atoms    1 box basis 5 2 basis 6 2 basis 7 2 basis 8 2
+Created 512 atoms
+  using lattice units in orthogonal box = (0 0 0) to (23.32 23.32 23.32)
+  create_atoms CPU = 0.001 seconds
+
+mass 1 114.76
+mass 2 30.98
+
+# POD potential
+pair_style pod
+pair_coeff * * InP_param.pod InP_coefficients.pod In P
+**************** Begin of POD Potentials ****************
+species: In P 
+periodic boundary conditions: 1 1 1
+number of environment clusters: 1
+number of principal compoments: 2
+inner cut-off radius: 0.8
+outer cut-off radius: 5
+bessel polynomial degree: 4
+inverse polynomial degree: 8
+one-body potential: 1
+two-body radial basis functions: 6
+three-body radial basis functions: 5
+three-body angular degree: 4
+four-body radial basis functions: 4
+four-body angular degree: 2
+five-body radial basis functions: 0
+five-body angular degree: 0
+six-body radial basis functions: 0
+six-body angular degree: 0
+seven-body radial basis functions: 0
+seven-body angular degree: 0
+number of local descriptors per element for one-body potential: 1
+number of local descriptors per element for two-body potential: 12
+number of local descriptors per element for three-body potential: 75
+number of local descriptors per element for four-body potential: 64
+number of local descriptors per element for five-body potential: 0
+number of local descriptors per element for six-body potential: 0
+number of local descriptors per element for seven-body potential: 0
+number of local descriptors per element for all potentials: 152
+number of global descriptors: 304
+**************** End of POD Potentials ****************
+
+**************** Begin of Model Coefficients ****************
+total number of coefficients for POD potential: 304
+total number of elements for PCA projection matrix: 0
+total number of elements for PCA centroids: 0
+**************** End of Model Coefficients ****************
+
+
+# Setup output
+
+thermo          10
+thermo_modify norm yes
+
+# Set up NVE run
+
+timestep 0.5e-3
+neighbor 1.0 bin
+neigh_modify once no every 1 delay 0 check yes
+
+# Run MD
+
+velocity all create 300.0 4928459 loop geom
+fix 1 all nve
+run             ${nsteps}
+run             100
+Neighbor list info ...
+  update: every = 1 steps, delay = 0 steps, check = yes
+  max neighbors/atom: 2000, page size: 100000
+  master list distance cutoff = 6
+  ghost atom cutoff = 6
+  binsize = 3, bins = 8 8 8
+  1 neighbor lists, perpetual/occasional/extra = 1 0 0
+  (1) pair pod, perpetual
+      attributes: full, newton on
+      pair build: full/bin/atomonly
+      stencil: full/bin/3d
+      bin: standard
+Per MPI rank memory allocation (min/avg/max) = 3.215 | 3.215 | 3.215 Mbytes
+   Step          Temp          E_pair         E_mol          TotEng         Press     
+         0   300           -4.8392777      0             -4.8005754      1561.0654    
+        10   291.27079     -4.8381515      0             -4.8005753      1709.509     
+        20   266.69372     -4.8349805      0             -4.8005749      2126.86      
+        30   230.86163     -4.8303573      0             -4.8005744      2735.6894    
+        40   190.64668     -4.8251686      0             -4.8005738      3416.9247    
+        50   153.9516      -4.8204341      0             -4.8005732      4022.2533    
+        60   127.93805     -4.8170778      0             -4.8005728      4405.9763    
+        70   117.12501     -4.8156828      0             -4.8005727      4475.6131    
+        80   122.09497     -4.8163242      0             -4.800573       4231.7934    
+        90   139.42686     -4.8185607      0             -4.8005735      3766.8505    
+       100   162.84813     -4.8215828      0             -4.8005741      3221.8605    
+Loop time of 0.818141 on 4 procs for 100 steps with 512 atoms
+
+Performance: 5.280 ns/day, 4.545 hours/ns, 122.228 timesteps/s, 62.581 katom-step/s
+94.0% CPU use with 4 MPI tasks x 1 OpenMP threads
+
+MPI task timing breakdown:
+Section |  min time  |  avg time  |  max time  |%varavg| %total
+---------------------------------------------------------------
+Pair    | 0.70717    | 0.7255     | 0.75748    |   2.2 | 88.68
+Neigh   | 0          | 0          | 0          |   0.0 |  0.00
+Comm    | 0.05765    | 0.088203   | 0.10797    |   6.3 | 10.78
+Output  | 0.00030107 | 0.00039215 | 0.00055987 |   0.0 |  0.05
+Modify  | 0.00051915 | 0.00059064 | 0.00069306 |   0.0 |  0.07
+Other   |            | 0.003452   |            |       |  0.42
+
+Nlocal:            128 ave         128 max         128 min
+Histogram: 4 0 0 0 0 0 0 0 0 0
+Nghost:            783 ave         783 max         783 min
+Histogram: 4 0 0 0 0 0 0 0 0 0
+Neighs:              0 ave           0 max           0 min
+Histogram: 4 0 0 0 0 0 0 0 0 0
+FullNghs:         4352 ave        4352 max        4352 min
+Histogram: 4 0 0 0 0 0 0 0 0 0
+
+Total # of neighbors = 17408
+Ave neighs/atom = 34
+Neighbor list builds = 0
+Dangerous builds = 0
+
+Total wall time: 0:00:00

examples/PACKAGES/pod/README.md

@@ -3,19 +3,36 @@
 Go to `lammps` directory and build with the POD package:
 
     cd path/to/lammps
-    mkdir build-pod
+    mkdir build
-    cd build-pod
+    cd build
     cmake -C ../cmake/presets/basic.cmake -D PKG_ML-POD=on ../cmake
     cmake --build .
 
-### Fit a POD potential for tantalum
+### Compile LAMMPS/POD with Kokkos 
+
+    cmake -C ../cmake/presets/basic.cmake -C ../cmake/presets/kokkos-cuda.cmake -D PKG_ML-POD=on ../cmake
+
+### Fit a POD potential for Tantalum
 
 Go to `lammps/examples/PACKAGES/pod/Ta` directory and run 
 
-    lmp -in in.podfit
+    lmp -in Ta_fit.pod
 
-See the README in `lammps/examples/PACKAGES/pod/Ta` for instructions on how to run MD with the potential.
+This creates `Ta_coefficients.pod` for the linear model, which we can use to run MD with
+
+    lmp -in Ta_mdrun.pod
+
+### Fit a POD potential for Indium Phosphide
+
+Go to `lammps/examples/PACKAGES/pod/InP` directory and run 
+
+    lmp -in InP_fit.pod
+
+This creates `InP_coefficients.pod` for the linear model, which we can use to run MD with
+
+    lmp -in InP_mdrun.pod
 
 ### Examples for other materials
 
 See [https://github.com/cesmix-mit/pod-examples](https://github.com/cesmix-mit/pod-examples)
+

examples/PACKAGES/pod/Ta/Ta_coeff.pod

@@ -1 +0,0 @@
-../../../../potentials/Ta_coeff.pod

examples/PACKAGES/pod/Ta/Ta_coeff.pod

@@ -0,0 +1,33 @@
+model_coefficients: 32 0 0
+-4.45745  
+29.40034  
+-13.69439 
+-0.32907  
+-0.14786  
+-1.35221  
+-0.59315  
+-26.30409 
+-33.37233 
+162.42473 
+144.67248 
+-149.50021
+1.78603   
+2.49026   
+-11.04768 
+-11.14333 
+12.40537  
+0.48284   
+0.39345   
+-2.25812  
+-1.38908  
+1.31551   
+0.02974   
+-0.05094  
+-0.21177  
+0.12127   
+0.23170   
+0.02426   
+-0.15305  
+-0.10803  
+0.25628   
+0.01291   

examples/PACKAGES/pod/Ta/Ta_coefficients.pod

@@ -1,33 +1,33 @@
-POD_coefficients: 32
+model_coefficients: 32 0 0
--4.44242  
+-4.45745  
-4.10219   
+29.40034  
-2.36987   
+-13.69439 
-3.92184   
+-0.32907  
--0.83796  
+-0.14786  
--0.79457  
+-1.35221  
--0.26230  
+-0.59315  
--21.24294 
+-26.30409 
--15.38460 
+-33.37233 
--38.44056 
+162.42473 
-8.29872   
+144.67248 
--42.54514 
+-149.50021
-2.79976   
+1.78603   
-3.76109   
+2.49026   
-5.23499   
+-11.04768 
-0.04878   
+-11.14333 
-2.96006   
+12.40537  
-0.09101   
+0.48284   
--0.19257  
+0.39345   
--0.24326  
+-2.25812  
--0.16735  
+-1.38908  
-0.53738   
+1.31551   
-0.02236   
+0.02974   
--0.00154  
+-0.05094  
-0.02488   
+-0.21177  
--0.00565  
+0.12127   
-0.07672   
+0.23170   
--0.05894  
+0.02426   
--0.05604  
+-0.15305  
--0.12664  
+-0.10803  
-0.11723   
+0.25628   
-0.00262   
+0.01291   

examples/PACKAGES/pod/Ta/Ta_data.pod

@@ -3,10 +3,11 @@ file_extension xyz
 
 path_to_training_data_set "XYZ"
 path_to_test_data_set "XYZ"
+path_to_environment_configuration_set "XYZ"
 
 fitting_weight_energy 100.0
 fitting_weight_force 1.0
-fitting_regularization_parameter 1e-10
+fitting_regularization_parameter 1e-12
 
 error_analysis_for_training_data_set 1
 error_analysis_for_test_data_set 0
@@ -17,4 +18,3 @@ basename_for_output_files Ta
 # number of digits after the decimal point for pod coefficients
 precision_for_pod_coefficients 5
 
-

examples/PACKAGES/pod/Ta/Ta_param.pod

@@ -1,4 +1,3 @@
-# DATE: 2022-11-30 UNITS: metal CONTRIBUTOR: Ngoc Cuong Nguyen, exapde@gmail.com CITATION:  https://arxiv.org/abs/2209.02362
 # chemical element symbols
 species Ta
 
@@ -11,22 +10,37 @@ rin 1.0
 # outer cut-off radius
 rcut 5.0
 
+# use only for enviroment-adaptive potentials
+number_of_environment_clusters 1
+
+# principal_components of local descriptors
+number_of_principal_components 2
+
 # polynomial degrees for radial basis functions
 bessel_polynomial_degree 3
 inverse_polynomial_degree 6
 
-# one-body potential
-onebody 1
-
 # two-body linear POD potential
 twobody_number_radial_basis_functions 6
 
 # three-body linear POD potential
 threebody_number_radial_basis_functions 5
-threebody_number_angular_basis_functions 5
+threebody_angular_degree 4
+
+# four-body linear POD potential
+fourbody_number_radial_basis_functions 0
+fourbody_angular_degree 0
+
+# five-body linear POD potential
+fivebody_number_radial_basis_functions 0
+fivebody_angular_degree 0
+
+# six-body linear POD potential
+sixbody_number_radial_basis_functions 0
+sixbody_angular_degree 0
+
+# seven-body linear POD potential
+sevenbody_number_radial_basis_functions 0
+sevenbody_angular_degree 0
 
-# four-body linear SNAP potential
-fourbody_snap_twojmax 0 
 
-# quadratic POD potential
-quadratic_pod_potential 0

examples/PACKAGES/pod/Ta/Ta_training_analysis.pod

@@ -1,387 +1,387 @@
 # Displaced_A15.xyz
-  config   # atoms      energy        DFT energy     energy error     force          DFT force       force error
+  config   # atoms       volume        energy        DFT energy     energy error     force          DFT force       force error
-     1         64    -753.4412087    -754.220443     0.01217553565   7.734608752     8.398670477     0.1147177501    
+     1         64    1191.016129     -753.1698421    -754.220443     0.01641563835   7.40295037      8.398670477     0.1439758999    
-     2         64    -752.99206      -753.865255     0.01364367179   8.845831302     9.134430545     0.128875643     
+     2         64    1191.016129     -752.7395784    -753.865255     0.01758869658   8.280515739     9.134430545     0.1607787343    
-     3         64    -753.3230789    -754.0221       0.01092220404   8.320493902     9.017261102     0.1155421197    
+     3         64    1191.016129     -753.08785      -754.0221       0.01459765574   7.697535492     9.017261102     0.1420603113    
-     4         64    -753.5972757    -754.279613     0.01066151964   7.709417684     8.381725092     0.1058659753    
+     4         64    1191.016129     -753.3517402    -754.279613     0.01449801277   7.132364917     8.381725092     0.1340575727    
-     5         64    -753.0554721    -753.777209     0.01127713895   8.89827564      9.478314477     0.1191609049    
+     5         64    1191.016129     -752.7757043    -753.777209     0.01564851147   8.360253864     9.478314477     0.1513006151    
-     6         64    -753.3515905    -754.048643     0.01089144564   7.808950564     8.465317938     0.1128142237    
+     6         64    1191.016129     -753.0381763    -754.048643     0.01578854208   7.591838888     8.465317938     0.1285134018    
-     7         64    -753.6515992    -754.317603     0.01040630929   7.441773668     8.127690491     0.1024025645    
+     7         64    1191.016129     -753.3574797    -754.317603     0.01500192578   7.082010429     8.127690491     0.1223953112    
-     8         64    -753.3305668    -753.969161     0.009978033993  8.524333384     9.425464952     0.1066300011    
+     8         64    1191.016129     -753.1004299    -753.969161     0.01357392266   7.903578432     9.425464952     0.1365521197    
-     9         64    -753.3982699    -754.141988     0.01162059588   8.165654685     8.821346913     0.1141641875    
+     9         64    1191.016129     -753.1947122    -754.141988     0.01480118465   7.516622986     8.821346913     0.1457127007    
 # Displaced_BCC.xyz
-  config   # atoms      energy        DFT energy     energy error     force          DFT force       force error
+  config   # atoms       volume        energy        DFT energy     energy error     force          DFT force       force error
-    10         54    -631.72742      -631.019667     0.01310653789   15.42892812     16.625876       0.264811012     
+    10         54    988.0479474     -631.5404329    -631.019667     0.009643812587  15.64136862     16.625876       0.2725503749    
-    11         54    -632.2725892    -631.719595     0.01024063328   14.51788198     15.58666626     0.2236637006    
+    11         54    988.0479474     -632.1993857    -631.719595     0.008885012437  14.51345042     15.58666626     0.2369926956    
-    12         54    -631.9431698    -631.386255     0.01031323642   15.21539049     15.92378883     0.2259171686    
+    12         54    988.0479474     -631.7954039    -631.386255     0.007576831115  15.20757603     15.92378883     0.2310810758    
-    13         54    -633.0728554    -632.575826     0.00920424781   13.38472946     14.55977162     0.2050161952    
+    13         54    988.0479474     -633.0131535    -632.575826     0.00809865759   13.46782392     14.55977162     0.2185066317    
-    14         54    -630.8933737    -630.450212     0.008206698429  16.5539163      16.96340726     0.2366453149    
+    14         54    988.0479474     -630.6309514    -630.450212     0.003347025529  17.00218411     16.96340726     0.2580441627    
-    15         54    -632.0739208    -631.669379     0.007491515672  15.23887638     16.05757315     0.2280333831    
+    15         54    988.0479474     -631.9637644    -631.669379     0.00545158078   15.32548025     16.05757315     0.2336752679    
-    16         54    -632.8030856    -632.431277     0.006885343815  14.21127984     14.69810718     0.2026063598    
+    16         54    988.0479474     -632.6507522    -632.431277     0.004064355464  14.35795151     14.69810718     0.2158812969    
-    17         54    -631.6814096    -630.960068     0.01335817778   14.70924474     15.99073148     0.2283605143    
+    17         54    988.0479474     -631.5521869    -630.960068     0.0109651643    14.75319251     15.99073148     0.2285673047    
-    18         54    -625.0410285    -623.378198     0.03079315656   23.39224423     24.67640432     0.3504654115    
+    18         54    988.0479474     -624.854495     -623.378198     0.02733883252   23.58927768     24.67640432     0.3545478911    
 # Displaced_FCC.xyz
-  config   # atoms      energy        DFT energy     energy error     force          DFT force       force error
+  config   # atoms       volume        energy        DFT energy     energy error     force          DFT force       force error
-    19         48    -555.9696753    -555.899463     0.001462755232  6.079460735     6.084617063     0.07083484607   
+    19         48    889.0559462     -555.8989975    -555.899463     9.69792269e-06  6.387988875     6.084617063     0.07805905013   
-    20         48    -555.9506355    -555.922478     0.0005866147697 6.28112122      6.297071211     0.09285822038   
+    20         48    889.0559462     -555.8789297    -555.922478     0.000907256654  6.632232564     6.297071211     0.1040918647    
-    21         48    -555.8344979    -555.800269     0.000713101184  6.153574445     6.021098636     0.08137696888   
+    21         48    889.0559462     -555.7628778    -555.800269     0.0007789836645 6.45057814      6.021098636     0.09471102034   
-    22         48    -556.2639568    -556.196151     0.00141262046   5.066504178     5.127955094     0.08649299664   
+    22         48    889.0559462     -556.2253041    -556.196151     0.0006073561042 5.301350042     5.127955094     0.09123176401   
-    23         48    -555.6269121    -555.488929     0.002874647697  6.848109843     7.050223459     0.08116202322   
+    23         48    889.0559462     -555.5406596    -555.488929     0.001077721414  7.195160551     7.050223459     0.08747135986   
-    24         48    -556.1089332    -556.027926     0.001687649405  5.662035842     5.611881174     0.07953916326   
+    24         48    889.0559462     -556.0330633    -556.027926     0.0001070272218 6.009103539     5.611881174     0.08935441647   
-    25         48    -556.0580873    -555.968399     0.001868505799  5.879931332     5.979217189     0.07470196865   
+    25         48    889.0559462     -555.9945281    -555.968399     0.0005443553218 6.212902066     5.979217189     0.081244274     
-    26         48    -556.0083267    -556.047132     0.0008084440258 5.752828608     5.544452585     0.08224848502   
+    26         48    889.0559462     -555.9554151    -556.047132     0.001910769529  6.012019145     5.544452585     0.09545132709   
-    27         48    -555.82441      -555.747848     0.001595040721  6.367423657     6.47892568      0.09497869851   
+    27         48    889.0559462     -555.7366233    -555.747848     0.0002338482448 6.764939057     6.47892568      0.1011665243    
 # Elastic_BCC.xyz
-  config   # atoms      energy        DFT energy     energy error     force          DFT force       force error
+  config   # atoms       volume        energy        DFT energy     energy error     force          DFT force       force error
-    28          2    -23.68353253    -23.689367      0.002917237243  0.0006486347527 0.0006222748589 7.696560647e-06 
+    28          2    36.40799882     -23.68590704    -23.689367      0.001729981765  0.0005857469375 0.0006222748589 9.806537327e-06 
-    29          2    -23.68281295    -23.689888      0.003537526523  0.0006442481331 0.0006166052222 7.353613433e-06 
+    29          2    36.47727251     -23.68481169    -23.689888      0.00253815708   0.0005821264542 0.0006166052222 8.797319207e-06 
-    30          2    -23.68293438    -23.689996      0.00353080996   0.0009115876426 0.0008810425642 1.183334558e-05 
+    30          2    36.47184897     -23.68494784    -23.689996      0.002524078869  0.0008240616654 0.0008810425642 2.037428468e-05 
-    31          2    -23.68108003    -23.690957      0.004938485589  1.044193543e-06 0               4.166082999e-07 
+    31          2    36.62078348     -23.68225087    -23.690957      0.004353065844  9.422546395e-07 0               3.770200667e-07 
-    32          2    -23.67919793    -23.690521      0.005661535829  0.0006261455712 0.0005982273815 7.573309962e-06 
+    32          2    36.71197042     -23.67989944    -23.690521      0.005310779451  0.000566950477  0.0005982273815 8.158760804e-06 
-    33          2    -23.67785535    -23.69038       0.006262326378  0.0006219476538 0.0005925723585 8.098703345e-06 
+    33          2    36.77593928     -23.67819051    -23.69038       0.00609474427   0.0005635032259 0.0005925723585 7.849374173e-06 
-    34          2    -23.68415292    -23.689202      0.00252453823   0.0006520193214 0.0006279363025 7.128171197e-06 
+    34          2    36.36547558     -23.68676383    -23.689202      0.001219083545  0.0005885128327 0.0006279363025 1.053580541e-05 
-    35          2    -23.68169552    -23.690482      0.004393238412  0.0009021557258 0.0008640138888 1.329061297e-05 
+    35          2    36.55974375     -23.68319963    -23.690482      0.003641183354  0.000815464884  0.0008640138888 1.662920456e-05 
-    36          2    -23.68301023    -23.689902      0.003445886213  0.0006432418939 0.0006152154094 8.589463686e-06 
+    36          2    36.46414346     -23.68507116    -23.689902      0.002415420054  0.0005812774047 0.0006152154094 9.669302107e-06 
-    37          2    -23.68063814    -23.690563      0.004962429905  0.0006318669831 0.0006038725031 7.463726891e-06 
+    37          2    36.63368821     -23.6817672     -23.690563      0.004397900334  0.0005717456253 0.0006038725031 8.311567538e-06 
-    38          2    -23.68337588    -23.690207      0.003415557958  0.001118071502  0.00107369735   1.811741272e-05 
+    38          2    36.45345189     -23.68547117    -23.690207      0.002367914312  0.001009744333  0.00107369735   2.610693709e-05 
-    39          2    -23.68369233    -23.689285      0.00279633424   0.0009215683923 0.000890013483  1.127366011e-05 
+    39          2    36.38484847     -23.68616091    -23.689285      0.001562044483  0.0008322058899 0.000890013483  1.991679691e-05 
-    40          2    -23.68344234    -23.689768      0.003162828655  0.001120158205  0.001080249045  1.630224161e-05 
+    40          2    36.43347895     -23.68567207    -23.689768      0.002047966899  0.001012061035  0.001080249045  2.782864008e-05 
-    41          2    -23.68224173    -23.68968       0.003719136062  0.0009070521506 0.0008680034562 1.339908745e-05 
+    41          2    36.50220719     -23.68411383    -23.68968       0.002783085738  0.0008199315614 0.0008680034562 1.637343483e-05 
-    42          2    -23.68259685    -23.690074      0.003738573623  0.00143649564   0.001373818765  2.432187597e-05 
+    42          2    36.50719109     -23.68445604    -23.690074      0.002808981302  0.001296718439  0.001373818765  2.64147971e-05  
-    43          2    -23.68469428    -23.688108      0.001706858485  0.0006587619148 0.0006336134468 7.932733888e-06 
+    43          2    36.28428565     -23.68777598    -23.688108      0.0001660085343 0.000594221946  0.0006336134468 1.099939509e-05 
-    44          2    -23.68405177    -23.689241      0.002594615211  0.0009223784492 0.0008880101351 1.189350098e-05 
+    44          2    36.3642236      -23.68663754    -23.689241      0.001301727662  0.0008329159633 0.0008880101351 1.874593476e-05 
-    45          2    -23.68384626    -23.68952       0.002836868987  0.0009181252225 0.0008860011287 1.116431522e-05 
+    45          2    36.40397469     -23.68626116    -23.68952       0.001629419996  0.0008297070704 0.0008860011287 1.917842744e-05 
-    46          2    -23.68524763    -23.686278      0.0005151850613 0.0006668258323 0.0006406777661 8.58562287e-06  
+    46          2    36.15958616     -23.68901859    -23.686278      0.001370293226  0.0006010646632 0.0006406777661 1.138305654e-05 
-    47          2    -23.67629396    -23.690097      0.006901518594  0.0008737523828 0.0008410160522 1.125104926e-05 
+    47          2    36.85012426     -23.6762264     -23.690097      0.006935298115  0.0007925625457 0.0008410160522 1.643998947e-05 
-    48          2    -23.67835169    -23.690811      0.006229654604  0.0008814028122 0.0008500070588 1.103963422e-05 
+    48          2    36.76983294     -23.67871264    -23.690811      0.006049181932  0.0007984019479 0.0008500070588 1.765059262e-05 
-    49          2    -23.67981574    -23.690266      0.005225130991  0.001091936388  0.001044322747  1.944706281e-05 
+    49          2    36.6630398      -23.68078335    -23.690266      0.004741323226  0.0009871892379 0.001044322747  2.331514572e-05 
-    50          2    -23.68209703    -23.690597      0.004249983197  0.001105769275  0.001050833003  2.242828165e-05 
+    50          2    36.55357619     -23.68366573    -23.690597      0.003465633435  0.0009975988347 0.001050833003  2.173210926e-05 
-    51          2    -23.68050418    -23.690673      0.005084408246  0.000631172526  0.0006038907186 7.85857762e-06  
+    51          2    36.65271066     -23.68154759    -23.690673      0.004562704504  0.0005710871669 0.0006038907186 8.900574077e-06 
-    52          2    -23.68185505    -23.690551      0.00434797299   0.0009022813915 0.0008590064028 1.486707593e-05 
+    52          2    36.56222224     -23.68337216    -23.690551      0.003589418943  0.0008144210952 0.0008590064028 1.523928952e-05 
-    53          2    -23.68191508    -23.690693      0.004388958442  0.0009013677777 0.0008590110593 1.516503239e-05 
+    53          2    36.56679849     -23.68340668    -23.690693      0.003643158311  0.0008137974304 0.0008590110593 1.595698248e-05 
-    54          2    -23.68097184    -23.69021       0.004619081961  0.0009000307855 0.0008730051546 9.670733045e-06 
+    54          2    36.59811665     -23.6823077     -23.69021       0.003951151804  0.0008145831598 0.0008730051546 2.003359235e-05 
-    55          2    -23.68426495    -23.688943      0.002339025274  0.0009232115961 0.0008800306813 1.619629586e-05 
+    55          2    36.34900278     -23.68697807    -23.688943      0.0009824644101 0.0008322110648 0.0008800306813 1.744870469e-05 
-    56          2    -23.67842316    -23.690136      0.005856419419  0.0006239138245 0.000593996633  8.394193459e-06 
+    56          2    36.74034826     -23.67898787    -23.690136      0.005574066484  0.0005652132989 0.000593996633  7.92587851e-06  
-    57          2    -23.6849427     -23.687444      0.001250651312  0.0009347957747 0.000903059245  1.290489522e-05 
+    57          2    36.23610366     -23.68828866    -23.687444      0.0004223293819 0.0008436278789 0.000903059245  2.177751265e-05 
-    58          2    -23.6836322     -23.689801      0.003084401813  0.0009160470298 0.0008740011442 1.424271291e-05 
+    58          2    36.42259639     -23.68591698    -23.689801      0.001942008249  0.0008265155784 0.0008740011442 1.602155127e-05 
-    59          2    -23.6814842     -23.690408      0.00446190038   8.690218902e-07 0               3.245696976e-07 
+    59          2    36.58194        -23.68291534    -23.690408      0.003746329075  7.853116414e-07 0               2.932806621e-07 
-    60          2    -23.68115817    -23.690362      0.004601914896  0.0006345480975 0.0006067503605 9.377221838e-06 
+    60          2    36.59950783     -23.68250113    -23.690362      0.003930433448  0.0005739954417 0.0006067503605 1.009250412e-05 
-    61          2    -23.67229452    -23.688881      0.008293240443  0.0008566684404 0.0008250054545 1.108928728e-05 
+    61          2    37.02589653     -23.67131384    -23.688881      0.008783582181  0.0007776878254 0.0008250054545 1.619373008e-05 
-    62          2    -23.6791352     -23.690515      0.005689901939  0.001534883496  0.001475779794  2.124695951e-05 
+    62          2    36.71189602     -23.67982686    -23.690515      0.005344069182  0.001390387166  0.001475779794  3.436613175e-05 
-    63          2    -23.67786743    -23.690551      0.006341785918  0.0006228264143 0.0005996599036 7.295416678e-06 
+    63          2    36.78962367     -23.67814275    -23.690551      0.006204123773  0.0005637977551 0.0005996599036 1.001095778e-05 
-    64          2    -23.68316372    -23.689487      0.003161641446  0.0006469755816 0.0006194384554 7.530154689e-06 
+    64          2    36.42642467     -23.68541088    -23.689487      0.002038057601  0.0005844344049 0.0006194384554 9.105178613e-06 
-    65          2    -23.6834063     -23.68986       0.003226849907  0.0009142334935 0.0008860124153 1.052672488e-05 
+    65          2    36.4423543      -23.68559418    -23.68986       0.002132908295  0.0008266682194 0.0008860124153 2.074533254e-05 
-    66          2    -23.68377813    -23.689288      0.002754934411  0.00145229412   0.001396479144  1.702826801e-05 
+    66          2    36.39164409     -23.68624726    -23.689288      0.001520371922  0.001312283722  0.001396479144  2.724122629e-05 
-    67          2    -23.67700773    -23.690457      0.006724637324  0.0006187196638 0.0005939831647 7.080762895e-06 
+    67          2    36.83059874     -23.67704953    -23.690457      0.006703736699  0.0005605067938 0.0005939831647 8.903855256e-06 
-    68          2    -23.67552804    -23.689792      0.007131981721  0.0008698720997 0.0008340587509 1.418233126e-05 
+    68          2    36.8936692      -23.67527599    -23.689792      0.007258002565  0.000787658236  0.0008340587509 1.727027889e-05 
-    69          2    -23.67583966    -23.690006      0.007083167888  0.0006146073806 0.0005897694465 8.07065747e-06  
+    69          2    36.88495742     -23.67562381    -23.690006      0.007191094218  0.0005570824127 0.0005897694465 9.526352044e-06 
-    70          2    -23.6777397     -23.690571      0.006415648131  0.0006207500925 0.0005939781141 7.401996527e-06 
+    70          2    36.7928657      -23.67798232    -23.690571      0.00629434147   0.0005623157716 0.0005939781141 8.388724073e-06 
-    71          2    -23.68270064    -23.690213      0.003756180649  0.001112284016  0.001084315452  1.142137177e-05 
+    71          2    36.50844234     -23.6845524     -23.690213      0.002830300186  0.001007417856  0.001084315452  3.13901245e-05  
-    72          2    -23.67870666    -23.690617      0.005955171449  0.0006250314539 0.0006024682564 6.623275772e-06 
+    72          2    36.74419477     -23.67922697    -23.690617      0.005695015742  0.0005656413796 0.0006024682564 9.800558604e-06 
-    73          2    -23.68231586    -23.689761      0.00372256923   0.0009095463313 0.0008790688255 1.222939687e-05 
+    73          2    36.49448266     -23.68420852    -23.689761      0.002776239615  0.0008225588858 0.0008790688255 2.057348461e-05 
-    74          2    -23.67673328    -23.69027       0.006768359835  7.188704983e-07 0               2.129270726e-07 
+    74          2    36.83933705     -23.67673911    -23.69027       0.006765442668  6.51984476e-07  0               1.932645324e-07 
-    75          2    -23.68164707    -23.690599      0.004475963334  0.0006376044826 0.0006137752031 6.574310078e-06 
+    75          2    36.5709148      -23.68309624    -23.690599      0.003751378046  0.0005763054751 0.0006137752031 9.640531893e-06 
-    76          2    -23.67997815    -23.69061       0.00531592353   9.698202031e-07 0               3.95870452e-07  
+    76          2    36.67683082     -23.68088394    -23.69061       0.004863030461  8.763722169e-07 0               3.577227741e-07 
-    77          2    -23.68008634    -23.690603      0.005258328411  0.0008923489326 0.0008590331775 1.256831367e-05 
+    77          2    36.66115635     -23.68104805    -23.690603      0.004777472809  0.0008071491031 0.0008590331775 1.853779451e-05 
-    78          2    -23.68488966    -23.687908      0.001509170978  0.0009340324028 0.0009010105438 1.204104822e-05 
+    78          2    36.25583797     -23.68810086    -23.687908      9.643173451e-05 0.0008433322094 0.0009010105438 2.010525612e-05 
-    79          2    -23.6795094     -23.690688      0.005589299031  0.0008890828456 0.0008470064935 1.419626566e-05 
+    79          2    36.69315685     -23.68027964    -23.690688      0.005204178753  0.0008040458508 0.0008470064935 1.442630316e-05 
-    80          2    -23.68316126    -23.689988      0.003413372454  0.0006451612224 0.0006194465272 7.422528505e-06 
+    80          2    36.46769977     -23.68522986    -23.689988      0.002379071717  0.0005827976437 0.0006194465272 9.763878015e-06 
-    81          2    -23.68321956    -23.689613      0.003196718897  0.000912899593  0.0008740732235 1.539555522e-05 
+    81          2    36.44434113     -23.68541392    -23.689613      0.00209953858   0.0008243238033 0.0008740732235 1.862099135e-05 
-    82          2    -23.68181374    -23.690678      0.004432127652  0.0006373963006 0.0006123757017 7.454253265e-06 
+    82          2    36.57453003     -23.68327227    -23.690678      0.003702863528  0.0005762034709 0.0006123757017 9.833686501e-06 
-    83          2    -23.68196226    -23.69017       0.004103870298  0.0009041773842 0.0008750051428 9.854119736e-06 
+    83          2    36.54218785     -23.68361157    -23.69017       0.003279215566  0.0008176791029 0.0008750051428 1.921467316e-05 
-    84          2    -23.68483517    -23.687892      0.001528413806  0.001142179928  0.001112070142  1.229243027e-05 
+    84          2    36.26350252     -23.68802292    -23.687892      6.545993121e-05 0.001032253376  0.001112070142  3.258468659e-05 
-    85          2    -23.68271169    -23.690132      0.003710155487  0.0009085291666 0.000868018433  1.49999647e-05  
+    85          2    36.49725495     -23.68460293    -23.690132      0.002764534398  0.0008196684225 0.000868018433  1.73736591e-05  
-    86          2    -23.68018066    -23.690843      0.005331170668  0.0006305009468 0.0006081134763 5.90881572e-06  
+    86          2    36.66468316     -23.68110857    -23.690843      0.004867214139  0.0005702307406 0.0006081134763 9.414220345e-06 
-    87          2    -23.67957976    -23.690598      0.005509118787  0.001259431767  0.001217674833  1.243374729e-05 
+    87          2    36.69098146     -23.68038294    -23.690598      0.005107529327  0.001139059342  0.001217674833  2.06566425e-05  
-    88          2    -23.67869549    -23.690656      0.005980257091  0.0006251939788 0.0006024765556 7.13023928e-06  
+    88          2    36.7498524      -23.67919254    -23.690656      0.005731731866  0.0005658199144 0.0006024765556 1.012824587e-05 
-    89          2    -23.67884961    -23.690254      0.005702197143  0.001084797449  0.001043496047  1.68662339e-05  
+    89          2    36.72620595     -23.67950048    -23.690254      0.005376762214  0.0009822281627 0.001043496047  2.500732518e-05 
-    90          2    -23.67961701    -23.690694      0.005538492834  0.0006273834422 0.0006010740387 8.134278748e-06 
+    90          2    36.7046344      -23.68037755    -23.690694      0.00515822503   0.0005678245812 0.0006010740387 9.481625137e-06 
-    91          2    -23.68202458    -23.690097      0.004036211359  0.0009041492449 0.0008730234819 1.169617364e-05 
+    91          2    36.53215524     -23.6837194     -23.690097      0.00318880242   0.0008183268201 0.0008730234819 1.936710758e-05 
-    92          2    -23.68476212    -23.688402      0.001819942156  0.0006575509652 0.000632180354  7.7469499e-06   
+    92          2    36.28988463     -23.68778953    -23.688402      0.000306233365  0.0005932101303 0.000632180354  1.068318322e-05 
-    93          2    -23.68425036    -23.688669      0.002209320265  0.001133553123  0.001092474256  1.677033392e-05 
+    93          2    36.330155       -23.68704981    -23.688669      0.0008095957127 0.001023514967  0.001092474256  2.815195409e-05 
-    94          2    -23.68017683    -23.690538      0.005180583191  0.0008923392716 0.0008610145179 1.053989885e-05 
+    94          2    36.65451876     -23.68118381    -23.690538      0.004677093696  0.0008073441427 0.0008610145179 1.797964322e-05 
-    95          2    -23.68290142    -23.689722      0.003410287964  0.0006465597037 0.0006251287867 7.275875006e-06 
+    95          2    36.46623662     -23.68497164    -23.689722      0.002375180903  0.0005838510966 0.0006251287867 1.162407198e-05 
-    96          2    -23.6789537     -23.690581      0.005813649829  7.452601432e-07 0               2.355432868e-07 
+    96          2    36.73431174     -23.67954699    -23.690581      0.005517005254  6.747207861e-07 0               2.132659501e-07 
-    97          2    -23.6840847     -23.688755      0.002335150427  0.0006519723076 0.0006251143895 8.25078808e-06  
+    97          2    36.34544239     -23.68680631    -23.688755      0.0009743455055 0.0005885973278 0.0006251143895 1.022234556e-05 
-    98          2    -23.67367881    -23.689312      0.007816596299  0.0008618264365 0.0008290597083 1.323477647e-05 
+    98          2    36.9736935      -23.67299367    -23.689312      0.008159162687  0.0007819742447 0.0008290597083 1.76069415e-05  
-    99          2    -23.68489152    -23.687388      0.001248238956  0.001145929445  0.001120237475  1.049029355e-05 
+    99          2    36.24487417     -23.68822174    -23.687388      0.0004168686754 0.001036416473  0.001120237475  3.421810783e-05 
-   100          2    -23.68174648    -23.690664      0.004458761579  0.0006367386055 0.0006109402589 6.270984336e-06 
+   100          2    36.57555586     -23.68319244    -23.690664      0.003735779019  0.0005756998982 0.0006109402589 8.460885317e-06 
-   101          2    -23.67450636    -23.68941       0.007451817634  0.0006119997091 0.0005883553348 7.715800125e-06 
+   101          2    36.94151938     -23.67402837    -23.68941       0.00769081595   0.0005547944898 0.0005883553348 9.667605875e-06 
-   102          2    -23.68321442    -23.690035      0.003410290658  0.0009128748923 0.0008810062429 1.106310227e-05 
+   102          2    36.45547212     -23.68530561    -23.690035      0.002364692981  0.0008249402484 0.0008810062429 1.906781709e-05 
-   103          2    -23.67584952    -23.690015      0.007082738579  0.0008706222251 0.0008450195264 9.898495893e-06 
+   103          2    36.88496132     -23.67563424    -23.690015      0.007190382353  0.000790172518  0.0008450195264 1.940915801e-05 
-   104          2    -23.67856154    -23.690752      0.006095232174  0.0006245583967 0.0005996415596 7.033875201e-06 
+   104          2    36.76103389     -23.67899294    -23.690752      0.005879529841  0.0005653529749 0.0005996415596 9.061380987e-06 
-   105          2    -23.68297614    -23.689825      0.00342442945   0.0009134966073 0.0008800215906 1.147892484e-05 
+   105          2    36.45404349     -23.68506744    -23.689825      0.002378779626  0.0008251854421 0.0008800215906 1.852267093e-05 
-   106          2    -23.67876135    -23.690562      0.00590032283   0.0008849512172 0.0008560011682 1.005528708e-05 
+   106          2    36.74654739     -23.67929575    -23.690562      0.005633127253  0.000801763107  0.0008560011682 1.842443236e-05 
-   107          2    -23.67874342    -23.690622      0.005939288687  0.0008835043772 0.0008390017878 1.530603189e-05 
+   107          2    36.74084732     -23.67927675    -23.690622      0.005672626415  0.0007986783077 0.0008390017878 1.383930455e-05 
-   108          2    -23.6843441     -23.688764      0.002209950672  0.0009250850126 0.0008910185183 1.254407066e-05 
+   108          2    36.33025646     -23.68714468    -23.688764      0.0008096596348 0.0008354959994 0.0008910185183 1.950545073e-05 
-   109          2    -23.68340608    -23.690011      0.003302460748  0.0006464901241 0.0006194287691 7.216590251e-06 
+   109          2    36.44122368     -23.68556667    -23.690011      0.002222166915  0.0005839138329 0.0006194287691 9.095263256e-06 
-   110          2    -23.68476306    -23.687696      0.001466471271  0.001143422035  0.001087589996  2.279977174e-05 
+   110          2    36.25348342     -23.68799518    -23.687696      0.0001495917205 0.001029561919  0.001087589996  2.368346819e-05 
-   111          2    -23.67977853    -23.691019      0.005620235289  0.000888876189  0.0008540035129 1.1779733e-05   
+   111          2    36.69693588     -23.68052902    -23.691019      0.005244990763  0.0008045111684 0.0008540035129 1.660792245e-05 
-   112          2    -23.68440001    -23.689025      0.002312496017  6.723949094e-07 0               2.648676661e-07 
+   112          2    36.3425194      -23.68713615    -23.689025      0.0009444242204 6.048393422e-07 0               2.391864739e-07 
-   113          2    -23.68208689    -23.689952      0.003932553163  7.386833996e-07 0               2.88150653e-07  
+   113          2    36.51656499     -23.68385666    -23.689952      0.003047669619  6.637963301e-07 0               2.603475835e-07 
-   114          2    -23.67935439    -23.69061       0.005627806504  0.0008872685213 0.0008580011655 1.019979918e-05 
+   114          2    36.71447816     -23.68006157    -23.69061       0.005274216197  0.0008035446124 0.0008580011655 1.851139775e-05 
-   115          2    -23.68099138    -23.690595      0.004801812376  0.0008956193373 0.0008680069124 9.843191998e-06 
+   115          2    36.62519495     -23.68220128    -23.690595      0.004196860391  0.0008113491541 0.0008680069124 1.944419979e-05 
-   116          2    -23.67743565    -23.690231      0.006397673953  0.0006194343635 0.0005925892338 8.542917156e-06 
+   116          2    36.80154127     -23.67766382    -23.690231      0.006283590712  0.0005612910408 0.0005925892338 9.235122707e-06 
-   117          2    -23.67809541    -23.690469      0.006186797077  0.0008802359765 0.0008500294113 1.182654414e-05 
+   117          2    36.77742539     -23.67845523    -23.690469      0.006006884644  0.0007980880228 0.0008500294113 1.88002833e-05  
-   118          2    -23.68279142    -23.690482      0.003845288647  0.0009078436148 0.0008740102974 1.225600095e-05 
+   118          2    36.50183296     -23.68462479    -23.690482      0.002928604258  0.0008206653147 0.0008740102974 1.862862483e-05 
-   119          2    -23.67443144    -23.689613      0.007590778783  0.0008650318724 0.0008320192305 1.23538989e-05  
+   119          2    36.93568763     -23.67391526    -23.689613      0.007848867984  0.0007836859568 0.0008320192305 1.723468539e-05 
-   120          2    -23.68501591    -23.687426      0.001205043669  0.001145633567  0.00109577735   2.03694619e-05  
+   120          2    36.23289183     -23.68838681    -23.687426      0.0004804048231 0.001032041797  0.00109577735   2.600453853e-05 
-   121          2    -23.68302307    -23.689562      0.003269464306  0.0006474095532 0.0006265237426 6.532536015e-06 
+   121          2    36.44295904     -23.68519521    -23.689562      0.002183395162  0.0005844757167 0.0006265237426 1.128889659e-05 
-   122          2    -23.68134549    -23.6904        0.004527256823  4.272990756e-07 0               1.732352808e-07 
+   122          2    36.59751671     -23.68271637    -23.6904        0.003841815485  3.610825174e-07 0               1.4665868e-07   
-   123          2    -23.67843015    -23.690561      0.006065426647  0.0006235069318 0.0005982273815 6.816496585e-06 
+   123          2    36.76766724     -23.67885647    -23.690561      0.005852264977  0.0005645533896 0.0005982273815 8.625051998e-06 
-   124          2    -23.67292129    -23.689107      0.00809285397   0.0008589766346 0.0008180073349 1.439377155e-05 
+   124          2    37.00025894     -23.67207453    -23.689107      0.008516233835  0.0007781106616 0.0008180073349 1.390580399e-05 
-   125          2    -23.68123551    -23.690145      0.004454742608  0.0009009679944 0.0008740766557 1.132072203e-05 
+   125          2    36.58722353     -23.68265657    -23.690145      0.00374421628   0.0008159137665 0.0008740766557 2.136045675e-05 
-   126          2    -23.67777646    -23.690482      0.006352769316  0.0006215821083 0.0005939983165 8.362048689e-06 
+   126          2    36.79405605     -23.67803714    -23.690482      0.006222430293  0.0005630702013 0.0005939983165 8.85354297e-06  
-   127          2    -23.68318209    -23.689864      0.003340952886  0.0009142894487 0.0008860124153 1.044271435e-05 
+   127          2    36.45320348     -23.68530353    -23.689864      0.002280236365  0.0008267100988 0.0008860124153 2.061923922e-05 
 # Elastic_FCC.xyz
-  config   # atoms      energy        DFT energy     energy error     force          DFT force       force error
+  config   # atoms       volume        energy        DFT energy     energy error     force          DFT force       force error
-   128          4    -46.449456      -46.437936      0.002880000611  0.0007088173441 0.001265949446  0.0001573706237 
+   128          4    74.14589882     -46.45131085    -46.437936      0.003343711499  0.0008256456522 0.001265949446  0.0001479290162 
-   129          4    -46.45317307    -46.438504      0.003667267825  0.0007210982328 0.001492549497  0.0002032393675 
+   129          4    74.26852111     -46.45483689    -46.438504      0.00408322283   0.0008748833702 0.001492549497  0.0001669960806 
-   130          4    -46.44686167    -46.436378      0.002620918523  0.0004870837365 0.000810592376  0.0001107544174 
+   130          4    74.05957274     -46.44875622    -46.436378      0.00309455485   0.0005424811735 0.000810592376  0.0001015808542 
-   131          4    -46.45357979    -46.441551      0.003007196305  0.0008634182131 0.001283675193  0.0001231453909 
+   131          4    74.30647158     -46.45520791    -46.441551      0.003414228451  0.001024641     0.001283675193  8.610021967e-05 
-   132          4    -46.42409677    -46.416957      0.001784942313  0.0007481922079 0.001186145859  0.0001205918882 
+   132          4    73.40902276     -46.4265266     -46.416957      0.002392400067  0.0008639837782 0.001186145859  9.385948781e-05 
-   133          4    -46.45078882    -46.440495      0.002573455911  0.0007289008721 0.001212440514  0.0001119490174 
+   133          4    74.1804881      -46.45258342    -46.440495      0.003022104862  0.0008837693055 0.001212440514  7.54705377e-05  
-   134          4    -46.4501363     -46.437972      0.003041076136  0.001116532125  0.002358226452  0.0003166808771 
+   134          4    74.17596744     -46.45191353    -46.437972      0.00348538317   0.001290912634  0.002358226452  0.0002715207448 
-   135          4    -46.46241981    -46.44586       0.004139951294  0.001077737689  0.002033949852  0.0002702964015 
+   135          4    74.73528136     -46.46363987    -46.44586       0.004444967559  0.001259032014  0.002033949852  0.0002223899959 
-   136          4    -46.44743429    -46.435744      0.002922571394  0.0008383971706 0.001690849491  0.0002711013554 
+   136          4    74.0787509      -46.44925412    -46.435744      0.003377531217  0.0009337469328 0.001690849491  0.0002527015084 
-   137          4    -46.45237555    -46.438209      0.003541637787  0.0007039962535 0.001160049999  0.0001096430557 
+   137          4    74.24609528     -46.45412062    -46.438209      0.003977905441  0.0008183472184 0.001160049999  8.303212282e-05 
-   138          4    -46.43645451    -46.42629       0.002541127472  0.0004839683449 0.0005297018029 1.480491546e-05 
+   138          4    73.73005434     -46.43863377    -46.42629       0.003085943173  0.0005398665308 0.0005297018029 9.433755819e-06 
-   139          4    -46.45466199    -46.443301      0.002840247268  0.0008590849412 0.001818421568  0.0002395191538 
+   139          4    74.33993289     -46.45634184    -46.443301      0.003260209859  0.001019667847  0.001818421568  0.0002031714008 
-   140          4    -46.4513559     -46.439002      0.003088474484  0.000980675092  0.001416973535  0.0001142710898 
+   140          4    74.20715045     -46.45310823    -46.439002      0.003526557791  0.001120917878  0.001416973535  8.385490094e-05 
-   141          4    -46.44224357    -46.432438      0.00245139227   0.0008958100898 0.001010469198  5.862303988e-05 
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+   213          4    73.99983876     -46.44675075    -46.434009      0.00318543858   0.0009993979373 0.001391131194  0.000126864771  
-   214          4    -46.44732696    -46.436262      0.002766239028  0.001116549362  0.002503347159  0.0003211377445 
+   214          4    74.07916779     -46.4492147     -46.436262      0.003238173905  0.0012911873    0.002503347159  0.0002946038716 
-   215          4    -46.44414241    -46.434505      0.002409352177  0.0008685662223 0.001041637173  4.942106462e-05 
+   215          4    73.94744484     -46.44611874    -46.434505      0.0029034362    0.0009930846846 0.001041637173  1.44560542e-05  
-   216          4    -46.45095913    -46.438768      0.003047783488  0.0008482298138 0.001098285027  8.657909629e-05 
+   216          4    74.2021224      -46.45267242    -46.438768      0.003476105557  0.0009790325482 0.001098285027  5.900684038e-05 
-   217          4    -46.45111242    -46.440254      0.002714605501  0.0004892442432 0.0006069892915 5.824568303e-05 
+   217          4    74.20389194     -46.45287404    -46.440254      0.003155011025  0.0005440222637 0.0006069892915 4.917760806e-05 
-   218          4    -46.43463407    -46.42286       0.002943517186  0.0004976409931 0.0007365242698 7.564906264e-05 
+   218          4    73.66782167     -46.43682196    -46.42286       0.003490490208  0.0005521691303 0.0007365242698 6.657586723e-05 
-   219          4    -46.42611144    -46.418078      0.002008360417  0.001053243552  0.002028412187  0.0002473380313 
+   219          4    73.46349993     -46.42843317    -46.418078      0.002588792975  0.001215695483  0.002028412187  0.0002117690174 
-   220          4    -46.45344976    -46.440513      0.003234189608  0.0007024129954 0.001158189967  0.0001371889048 
+   220          4    74.30307454     -46.45509879    -46.440513      0.003646448628  0.0008205757569 0.001158189967  0.000110036346  
-   221          4    -46.41584187    -46.409824      0.001504467167  0.0007558580012 0.001759573812  0.0002386003087 
+   221          4    73.21819832     -46.41838058    -46.409824      0.002139145869  0.000869266353  0.001759573812  0.0002125030952 
-   222          4    -46.45494987    -46.440329      0.003655216631  0.0005034620022 0.0009534044263 0.0001064495091 
+   222          4    74.35772636     -46.45658501    -46.440329      0.004064003047  0.0006179175264 0.0009534044263 8.737057714e-05 
-   223          4    -46.45000759    -46.43773       0.003069396495  0.0006831478015 0.000926180328  7.390298375e-05 
+   223          4    74.17615527     -46.45177345    -46.43773       0.003510862689  0.0007631781991 0.000926180328  6.446679043e-05 
-   224          4    -46.42538863    -46.416525      0.002215907169  0.0005605993692 0.0007573664899 5.946405938e-05 
+   224          4    73.43860935     -46.4277585     -46.416525      0.002808375906  0.0006623119965 0.0007573664899 4.251239635e-05 
-   225          4    -46.45386072    -46.440293      0.003391930454  0.0006980795454 0.0007725386722 1.86450807e-05  
+   225          4    74.31356506     -46.45553467    -46.440293      0.003810416894  0.0008201864367 0.0007725386722 1.244767351e-05 
-   226          4    -46.4527969     -46.43839       0.003601726069  0.0005103417187 0.0005612022808 1.656002337e-05 
+   226          4    74.25452523     -46.45450406    -46.43839       0.004028515986  0.000624431309  0.0005612022808 1.898088401e-05 
-   227          4    -46.45374294    -46.438916      0.00370673382   0.0006956794369 0.001650878554  0.0002154167998 
+   227          4    74.27331932     -46.45546024    -46.438916      0.004136060657  0.0008098609869 0.001650878554  0.0001889274693 
 # GSF_110.xyz
-  config   # atoms      energy        DFT energy     energy error     force          DFT force       force error
+  config   # atoms       volume        energy        DFT energy     energy error     force          DFT force       force error
-   228         24    -278.7403996    -279.068761     0.01368172569   2.282668754     1.756353161     0.0474563559    
+   228         24    828.0362386     -278.8410589    -279.068761     0.009487586046  2.726148177     1.756353161     0.06344241374   
-   229         24    -279.902595     -279.784296     0.004929123882  0.9479314831    0.9057668891    0.02403120774   
+   229         24    828.0362386     -280.0438878    -279.784296     0.01081632552   1.025836691     0.9057668891    0.03431923408   
-   230         24    -279.9942014    -279.901657     0.003856015841  0.2795933118    0.001565946359  0.01120665859   
+   230         24    828.0362386     -280.1389453    -279.901657     0.009887011104  0.3820870056    0.001565946359  0.02063932212   
-   231         24    -279.6335344    -279.584238     0.002054016531  1.573004204     1.035572248     0.05514377891   
+   231         24    828.0362386     -279.7578636    -279.584238     0.007234400289  1.646483877     1.035572248     0.06317254006   
-   232         24    -279.9025974    -279.784283     0.004929767703  0.947921084     0.9056396189    0.02406018404   
+   232         24    828.0362386     -280.0438905    -279.784283     0.01081698125   1.025825697     0.9056396189    0.03433377902   
-   233         24    -279.1817177    -279.302158     0.005018345952  2.388096516     1.771965137     0.06275542538   
+   233         24    828.0362386     -279.2779929    -279.302158     0.001006879708  2.597392642     1.771965137     0.07498219236   
-   234         24    -279.5900705    -279.55564      0.001434605813  1.950503627     1.405626506     0.05370441115   
+   234         24    828.0362386     -279.7119341    -279.55564      0.006512252548  2.085996302     1.405626506     0.06414553539   
-   235         24    -279.0106063    -279.246939     0.00984719392   1.577003357     0.4813964151    0.08190583543   
+   235         24    828.0362386     -279.1342144    -279.246939     0.004696857796  1.7145726       0.4813964151    0.09091186796   
-   236         24    -279.1817217    -279.302157     0.005018138375  2.388094324     1.771953347     0.06275588675   
+   236         24    828.0362386     -279.2779974    -279.302157     0.001006650079  2.59739139      1.771953347     0.07498197018   
-   237         24    -279.0107548    -279.246935     0.009840841347  1.576191869     0.4809484798    0.0819682416    
+   237         24    828.0362386     -279.1342234    -279.246935     0.004696316576  1.714140427     0.4809484798    0.09087969403   
-   238         24    -279.9941671    -279.896025     0.004089255845  0.2809227604    0.01060549839   0.01118927817   
+   238         24    828.0362386     -280.1388645    -279.896025     0.01011831143   0.3833172699    0.01060549839   0.0205724723    
-   239         24    -279.6337951    -279.584237     0.002064919631  1.571895405     1.035836121     0.05510997377   
+   239         24    828.0362386     -279.7581378    -279.584237     0.007245866604  1.645952103     1.035836121     0.06318595533   
-   240         24    -278.8616595    -279.124427     0.0109486445    2.383512182     1.809545887     0.06232801199   
+   240         24    828.0362386     -278.9562357    -279.124427     0.007007972259  2.699607205     1.809545887     0.07438804482   
-   241         24    -279.2927133    -279.379366     0.003610531084  1.779238829     0.8982692706    0.07658702105   
+   241         24    828.0362386     -279.4052861    -279.379366     0.00108000439   1.874556392     0.8982692706    0.08646596743   
-   242         24    -279.292656     -279.37937      0.003613082676  1.779203263     0.898081355     0.0765940488    
+   242         24    828.0362386     -279.4051598    -279.37937      0.001074574944  1.874858028     0.898081355     0.08649971418   
-   243         24    -278.8616573    -279.124427     0.01094873842   2.383511745     1.809523374     0.06232387507   
+   243         24    828.0362386     -278.9562334    -279.124427     0.007008065732  2.699608673     1.809523374     0.07438947193   
-   244         24    -279.9942014    -279.901657     0.003856015842  0.27959331      0.001570374478  0.01120603916   
+   244         24    828.0362386     -280.1389453    -279.901657     0.009887011104  0.382087008     0.001570374478  0.02063718463   
-   245         24    -279.9072278    -279.79264      0.004774491325  0.8361247356    0.8392614852    0.02418251879   
+   245         24    828.0362386     -280.0482205    -279.79264      0.01064918897   0.9069086057    0.8392614852    0.03243659951   
-   246         24    -279.9941671    -279.896025     0.004089255843  0.2809227622    0.01060243293   0.01118973247   
+   246         24    828.0362386     -280.1388645    -279.896025     0.01011831143   0.3833172675    0.01060243293   0.02057250032   
-   247         24    -278.8973689    -279.206496     0.01288029691   1.390234609     0.005326518563  0.06648378416   
+   247         24    828.0362386     -279.0366628    -279.206496     0.007076382361  1.638514407     0.005326518563  0.08048168704   
-   248         24    -279.590075     -279.55564      0.001434791018  1.950495712     1.4056319       0.05370353355   
+   248         24    828.0362386     -279.7119391    -279.55564      0.006512460902  2.085987992     1.4056319       0.06414586851   
-   249         24    -279.9072386    -279.79264      0.004774943229  0.8361385582    0.8392625708    0.02418484015   
+   249         24    828.0362386     -280.0482407    -279.79264      0.01065002958   0.9067922986    0.8392625708    0.03242814224   
 # GSF_112.xyz
-  config   # atoms      energy        DFT energy     energy error     force          DFT force       force error
+  config   # atoms       volume        energy        DFT energy     energy error     force          DFT force       force error
-   250         30    -345.1428414    -345.175835     0.001099787279  2.717783384     1.057395322     0.1393371019    
+   250         30    1075.650827     -344.9605863    -345.175835     0.007174958242  2.758670703     1.057395322     0.1516335449    
-   251         30    -346.8213325    -346.361714     0.01532061701   1.6320981       1.220284939     0.1010819808    
+   251         30    1075.650827     -346.7372372    -346.361714     0.01251744041   1.674795336     1.220284939     0.09596889278   
-   252         30    -346.3061373    -345.795524     0.01702044399   2.435031121     2.112860875     0.1171529224    
+   252         30    1075.650827     -346.1686186    -345.795524     0.0124364868    2.551456187     2.112860875     0.1075528655    
-   253         30    -344.8834516    -345.164602     0.009371679668  3.314987489     1.765832199     0.1576958872    
+   253         30    1075.650827     -344.7305027    -345.164602     0.01446997708   3.364761651     1.765832199     0.1653996104    
-   254         30    -346.9668291    -346.593523     0.01244353764   1.327935537     0.01148867129   0.08670065177   
+   254         30    1075.650827     -346.8954513    -346.593523     0.01006427628   1.339499001     0.01148867129   0.08728299447   
-   255         30    -346.7938009    -346.396186     0.01325383111   1.743989434     0.9954683928    0.09783463277   
+   255         30    1075.650827     -346.7069529    -346.396186     0.01035889705   1.846653887     0.9954683928    0.09979294451   
-   256         30    -345.0939055    -345.319406     0.007516682784  3.756566851     1.772040852     0.1806000978    
+   256         30    1075.650827     -344.9126927    -345.319406     0.01355711006   3.783666815     1.772040852     0.1835364962    
-   257         30    -345.6468551    -345.594794     0.001735368441  3.432645857     1.516014157     0.1670589876    
+   257         30    1075.650827     -345.4584504    -345.594794     0.004544785139  3.694055398     1.516014157     0.1747792869    
-   258         30    -346.2843474    -345.98566      0.00995624537   2.709563559     1.406252265     0.1356658489    
+   258         30    1075.650827     -346.1486771    -345.98566      0.005433903845  2.934925394     1.406252265     0.1397537934    
-   259         30    -345.7058793    -345.383994     0.01072951129   2.464665654     0.963574308     0.13389942      
+   259         30    1075.650827     -345.5181007    -345.383994     0.00447022439   2.558293398     0.963574308     0.1353120293    
-   260         30    -346.9664564    -346.582564     0.01279641284   1.32870642      0.0126740587    0.08670344939   
+   260         30    1075.650827     -346.8950741    -346.582564     0.01041700207   1.340303074     0.0126740587    0.08735503715   
-   261         30    -345.3305431    -345.452139     0.004053195139  4.515828739     2.787719406     0.1519418929    
+   261         30    1075.650827     -345.1232455    -345.452139     0.01096311715   4.843836394     2.787719406     0.158731815     
-   262         30    -346.966836     -346.593523     0.01244376534   1.327919807     0.01148834      0.08669988209   
+   262         30    1075.650827     -346.8954617    -346.593523     0.01006462208   1.339471584     0.01148834      0.08728175252   
-   263         30    -345.5935851    -345.281949     0.01038786965   2.922665543     1.873142686     0.1300383724    
+   263         30    1075.650827     -345.3878123    -345.281949     0.003528777779  3.04388336      1.873142686     0.1266226401    
-   264         30    -346.157169     -345.928661     0.007616932828  3.42803556      2.100874472     0.1330089569    
+   264         30    1075.650827     -346.0211337    -345.928661     0.003082422836  3.704012447     2.100874472     0.1385926656    
-   265         30    -344.6836135    -345.111657     0.01426811685   4.87813643      3.358068319     0.1517605656    
+   265         30    1075.650827     -344.4666474    -345.111657     0.0215003205    5.060940978     3.358068319     0.1556709723    
-   266         30    -346.8140968    -346.367123     0.01489912587   1.700448289     1.335797131     0.1014030448    
+   266         30    1075.650827     -346.731384     -346.367123     0.01214203185   1.743704774     1.335797131     0.0964003512    
-   267         30    -346.9664062    -346.582565     0.0127947081    1.328695393     0.01254743735   0.08670444025   
+   267         30    1075.650827     -346.8950084    -346.582565     0.0104147809    1.34025766      0.01254743735   0.08735400875   
-   268         30    -344.5284456    -344.91356      0.012837147     4.30679737      3.441834403     0.1293440404    
+   268         30    1075.650827     -344.3283906    -344.91356      0.01950564575   4.516603649     3.441834403     0.1385132929    
-   269         30    -346.3471173    -345.836703     0.01701381162   2.177883948     1.608769148     0.1178087924    
+   269         30    1075.650827     -346.2085633    -345.836703     0.01239534254   2.265804409     1.608769148     0.108126121     
-   270         30    -344.9135302    -344.984307     0.002359225816  3.517317775     2.542628782     0.122092966     
+   270         30    1075.650827     -344.700705     -344.984307     0.009453398382  3.625655349     2.542628782     0.1276641348    
-   271         30    -346.7846048    -346.393931     0.01302245877   1.941770224     1.211680725     0.09898842713   
+   271         30    1075.650827     -346.7005545    -346.393931     0.01022078221   2.065166442     1.211680725     0.1018842071    
 # Liquid.xyz
-  config   # atoms      energy        DFT energy     energy error     force          DFT force       force error
+  config   # atoms       volume        energy        DFT energy     energy error     force          DFT force       force error
-   272        100    -1104.74829     -1105.601723    0.008534329546  31.13590643     31.39853886     0.5826598142    
+   272        100    2002.996789     -1105.503318    -1105.601723    0.0009840495195 33.67286942     31.39853886     0.5196524511    
-   273        100    -1099.007356    -1099.673012    0.006656557481  34.30763539     32.03167218     0.6355970492    
+   273        100    2002.996789     -1100.916702    -1099.673012    0.01243689799   34.89745034     32.03167218     0.569788481     
-   274        100    -1123.744375    -1121.31506     0.0242931528    23.69463257     20.81076453     0.4843518851    
+   274        100    2002.996789     -1125.248108    -1121.31506     0.03933048075   23.1042808      20.81076453     0.4236223924    
 # Surface.xyz
-  config   # atoms      energy        DFT energy     energy error     force          DFT force       force error
+  config   # atoms       volume        energy        DFT energy     energy error     force          DFT force       force error
-   275         24    -279.9941674    -279.911828     0.003430809358  0.2809230274    0.002753093533  0.01155715982   
+   275         24    828.0362197     -280.1388649    -279.911828     0.009459870394  0.3833165637    0.002753093533  0.0209958793    
-   276         48    -551.0953781    -555.359452     0.08883487284   6.541312712     0.003020630398  0.1949601982    
+   276         48    1756.536679     -551.9765065    -555.359452     0.07047803038   5.695770431     0.003020630398  0.1710474815    
-   277         40    -458.209131     -459.216162     0.02517577443   5.605061426     5.0461364       0.1098503638    
+   277         40    1394.433693     -457.8965908    -459.216162     0.03298927919   6.47605009      5.0461364       0.1141155284    
-   278         40    -459.8554229    -461.144076     0.03221632783   2.691145822     0.005582740008  0.0817493       
+   278         40    1394.433693     -459.4317427    -461.144076     0.04280833158   2.948762022     0.005582740008  0.1122771088    
-   279         24    -279.8970746    -279.635146     0.01091369091   1.238573481     1.288799837     0.008644383713  
+   279         24    828.0362197     -279.9357878    -279.635146     0.01252674323   2.282528363     1.288799837     0.0489285834    
-   280         30    -346.9668295    -346.592525     0.01247681774   1.32793475      0.008446203407  0.08664452133   
+   280         30    1075.65076      -346.8954518    -346.592525     0.01009756105   1.339498529     0.008446203407  0.08713647389   
-   281         30    -345.8871537    -345.744506     0.004754921864  3.992236552     3.124961367     0.08594721633   
+   281         30    1075.65076      -345.7511061    -345.744506     0.0002200037964 4.894457614     3.124961367     0.1246204459    
 # Volume_A15.xyz
-  config   # atoms      energy        DFT energy     energy error     force          DFT force       force error
+  config   # atoms       volume        energy        DFT energy     energy error     force          DFT force       force error
-   282          8    -66.46788051    -66.990732      0.06535643627   8.928342366e-15 0               1.501728429e-15 
+   282          8    300.763         -66.50302875    -66.990732      0.06096290674   1.941277332e-14 0               3.37325783e-15  
-   283          8    -72.67646146    -72.957807      0.03516819273   3.04869178e-14  0               5.1001593e-15   
+   283          8    97.336          -72.75000964    -72.957807      0.0259746695    1.351006698e-13 0               2.177344384e-14 
-   284          8    -94.20621366    -94.145745      0.00755858243   1.880283026e-14 0               2.444387059e-15 
+   284          8    140.608         -94.15533163    -94.145745      0.001198328985  4.044529328e-14 0               6.693247629e-15 
-   285          8    -94.43981933    -94.554682      0.01435783313   5.684495802e-15 0               8.992080697e-16 
+   285          8    148.877         -94.40707977    -94.554682      0.01845027858   6.513916874e-14 0               1.052717644e-14 
-   286          8    -79.39814886    -79.438363      0.005026767696  1.186991025e-14 0               1.998979685e-15 
+   286          8    103.823         -79.45083178    -79.438363      0.001558598047  1.722214314e-13 0               2.77785865e-14  
-   287          8    -69.38946962    -69.627817      0.02979342197   5.582708452e-15 0               9.058870552e-16 
+   287          8    287.496         -69.43914664    -69.627817      0.02358379473   1.869801108e-14 0               2.486725909e-15 
-   288          8    -83.05531805    -82.604907      0.05630138147   5.067400154e-15 0               8.060681752e-16 
+   288          8    226.981         -83.07759076    -82.604907      0.05908546939   1.580586786e-14 0               2.506150792e-15 
-   289          8    14.36690687     14.89048        0.0654466408    7.096605716e-14 0               9.778491674e-15 
+   289          8    64              14.38834339     14.89048        0.06276707625   3.142551462e-13 0               4.611672661e-14 
-   290          8    -94.13472519    -94.367599      0.02910922586   1.767991013e-14 0               2.1395518e-15   
+   290          8    157.464         -94.121065      -94.367599      0.03081674996   4.627906691e-14 0               7.060581015e-15 
-   291          8    -89.38757156    -89.248227      0.01741807051   8.884610804e-15 0               1.30769238e-15  
+   291          8    195.112         -89.39236133    -89.248227      0.01801679107   2.992297744e-14 0               4.401789389e-15 
-   292          8    -87.49741165    -87.211997      0.03567683079   8.006170389e-15 0               1.152290069e-15 
+   292          8    205.379         -87.50415023    -87.211997      0.03651915426   2.29993221e-14  0               3.752044138e-15 
-   293          8    -93.42285179    -93.66897       0.03076477666   2.280172604e-15 0               3.891032311e-16 
+   293          8    166.375         -93.42125038    -93.66897       0.03096495278   2.907694533e-14 0               4.724788551e-15 
-   294          8    -8.05187323     -7.989166       0.007838403785  7.482512497e-14 0               1.195728177e-14 
+   294          8    68.921          -8.019333034    -7.989166       0.003770879216  3.356694228e-13 0               6.09434176e-14  
-   295          8    -85.3779751     -84.982834      0.04939263793   3.220622406e-15 0               4.863008144e-16 
+   295          8    216             -85.39060668    -84.982834      0.0509715856    9.263122354e-15 0               1.424782104e-15 
-   296          8    -92.37490481    -92.536373      0.0201835236    1.673164165e-14 0               2.290124109e-15 
+   296          8    175.616         -92.37850178    -92.536373      0.01973390211   3.567976799e-14 0               6.038472675e-15 
-   297          8    -26.56925158    -26.77612       0.02585855302   4.751528484e-14 0               7.423756449e-15 
+   297          8    74.088          -26.52314912    -26.77612       0.03162135966   2.830510779e-13 0               4.116147259e-14 
-   298          8    -77.90929192    -77.544107      0.04564811452   4.617032687e-15 0               7.294873617e-16 
+   298          8    250.047         -77.95455874    -77.544107      0.05130646772   1.722828231e-14 0               2.531351199e-15 
-   299          8    -80.55632181    -80.114217      0.05526310126   8.324980615e-15 0               1.201946528e-15 
+   299          8    238.328         -80.59031991    -80.114217      0.05951286389   1.790178605e-14 0               2.961270842e-15 
-   300          8    -41.83202596    -42.143041      0.03887688062   3.384606082e-14 0               5.356279237e-15 
+   300          8    79.507          -41.81723354    -42.143041      0.04072593188   2.017987815e-13 0               3.254206583e-14 
-   301          8    -91.02235339    -91.040671      0.002289700675  3.337550263e-15 0               5.490399801e-16 
+   301          8    185.193         -91.02736742    -91.040671      0.001662947812  2.413722535e-14 0               4.098218376e-15 
-   302          8    -84.76781055    -84.499231      0.03357244376   3.246108052e-14 0               5.927694678e-15 
+   302          8    110.592         -84.77992099    -84.499231      0.035086249     6.257383276e-14 0               9.730565054e-15 
-   303          8    -60.71236154    -61.825173      0.1391014324    7.918599116e-15 0               1.30776466e-15  
+   303          8    328.509         -60.69292469    -61.825173      0.1415310384    2.336487667e-14 0               4.192320181e-15 
-   304          8    -91.5794594     -91.156873      0.05282330009   3.642169681e-15 0               5.988997276e-16 
+   304          8    125             -91.53133052    -91.156873      0.04680718995   4.580314378e-14 0               7.417918736e-15 
-   305          8    -54.28408457    -54.658744      0.04683242815   8.878350559e-14 0               1.511496461e-14 
+   305          8    85.184          -54.31160005    -54.658744      0.04339299436   2.081820808e-13 0               3.494754179e-14 
-   306          8    -72.29317827    -72.277255      0.00199040924   2.467731222e-15 0               3.339523392e-16 
+   306          8    274.625         -72.34854762    -72.277255      0.008911577286  3.722472678e-15 0               6.21411631e-16  
-   307          8    -75.14428628    -74.923334      0.02761903549   3.575872549e-15 0               5.510457542e-16 
+   307          8    262.144         -75.19753913    -74.923334      0.03427564069   1.368884593e-14 0               2.258168709e-15 
-   308          8    -64.41647714    -64.798066      0.04769860741   1.525236831e-14 0               2.48556962e-15  
+   308          8    91.125          -64.47776048    -64.798066      0.04003818964   1.208370656e-13 0               1.995060684e-14 
-   309          8    -93.29905733    -93.048342      0.03133941583   1.463792794e-14 0               2.408158856e-15 
+   309          8    132.651         -93.2347704     -93.048342      0.02330355033   5.798970328e-14 0               9.670321353e-15 
-   310          8    -63.56375833    -64.38702       0.1029077093    2.897725758e-15 0               5.108399236e-16 
+   310          8    314.432         -63.5755377     -64.38702       0.1014352879    7.556804155e-15 0               1.29652209e-15  
-   311          8    -88.81067445    -88.352871      0.05722543104   1.077500255e-14 0               1.707889472e-15 
+   311          8    117.649         -88.79067694    -88.352871      0.05472574302   7.470145864e-14 0               1.29226998e-14  
 # Volume_BCC.xyz
-  config   # atoms      energy        DFT energy     energy error     force          DFT force       force error
+  config   # atoms       volume        energy        DFT energy     energy error     force          DFT force       force error
-   312          2    -16.38936242    -16.763625      0.1871312901    5.164700352e-16 0               1.827242061e-16 
+   312          2    74.088          -16.41904746    -16.763625      0.172288768     8.881784197e-16 0               2.960594732e-16 
-   313          2    16.19675433     16.314145       0.05869533666   6.530646709e-14 0               1.921032777e-14 
+   313          2    13.824          16.2292442      16.314145       0.04245040205   6.132313711e-13 0               2.290852693e-13 
-   314          2    -21.24238574    -21.209071      0.01665736942   1.908874745e-15 0               7.170229344e-16 
+   314          2    27              -21.2109771     -21.209071      0.0009530502432 1.123466673e-14 0               3.552712694e-15 
-   315          2    -15.80560502    -15.780524      0.01254051029   3.122816732e-14 0               1.231252513e-14 
+   315          2    21.952          -15.82599793    -15.780524      0.02273696393   2.538428743e-13 0               1.020665034e-13 
-   316          2    -19.05526774    -19.002205      0.02653137194   7.555287577e-15 0               2.037557095e-15 
+   316          2    24.389          -19.01309058    -19.002205      0.005442789013  7.306210466e-15 0               2.50031477e-15  
-   317          2    -22.67434567    -22.620568      0.02688883674   1.349360652e-15 0               4.857225733e-16 
+   317          2    29.791          -22.67048776    -22.620568      0.02495988117   2.031435111e-14 0               8.215650382e-15 
-   318          2    4.04311049      4.096885        0.02688725502   1.772872048e-14 0               6.601201067e-15 
+   318          2    15.625          4.095802366     4.096885        0.0005413171271 6.359497134e-14 0               2.069640755e-14 
-   319          2    56.2105911      56.26276        0.02608445186   1.377801077e-13 0               4.795418557e-14 
+   319          2    10.648          56.21520101     56.26276        0.0237794968    6.137452342e-13 0               2.262703913e-13 
-   320          2    -22.55797904    -22.585113      0.01356697915   3.380715703e-15 0               1.276756478e-15 
+   320          2    46.656          -22.54194179    -22.585113      0.02158560454   1.006819876e-14 0               3.996802889e-15 
-   321          2    -21.75972417    -21.795501      0.0178884163    1.168374574e-15 0               4.533410684e-16 
+   321          2    50.653          -21.73865048    -21.795501      0.0284252602    1.776356839e-15 0               5.921189465e-16 
-   322          2    33.30678917     33.110078       0.09835558332   3.387360342e-14 0               9.173217741e-15 
+   322          2    12.167          33.26085588     33.110078       0.0753889407    1.720476052e-13 0               4.707345624e-14 
-   323          2    -20.82125169    -20.885998      0.0323731563    9.918492908e-16 0               3.654484123e-16 
+   323          2    54.872          -20.80030783    -20.885998      0.04284508708   1.538370149e-15 0               5.921189465e-16 
-   324          2    -23.55239721    -23.601336      0.02446939304   2.356479148e-15 0               7.090682208e-16 
+   324          2    39.304          -23.54386901    -23.601336      0.02873349282   4.528839094e-15 0               1.480297366e-15 
-   325          2    -23.17147126    -23.207313      0.01792086946   1.448170847e-15 0               4.901445524e-16 
+   325          2    42.875          -23.16144784    -23.207313      0.02293258231   2.082963029e-15 0               7.401486831e-16 
-   326          2    -19.78146338    -19.898089      0.05831281177   7.349099448e-15 0               2.984880861e-15 
+   326          2    59.319          -19.76694674    -19.898089      0.06557112796   4.389974022e-14 0               1.776356839e-14 
-   327          2    -23.45038238    -23.405474      0.02245418985   2.124472575e-15 0               7.6356745e-16   
+   327          2    32.768          -23.46365391    -23.405474      0.0290899572    1.331156944e-14 0               5.403085387e-15 
-   328          2    -4.653232293    -4.781324       0.06404585371   1.121589994e-14 0               3.980033895e-15 
+   328          2    17.576          -4.6700202      -4.781324       0.05565189983   4.987657631e-14 0               1.465494393e-14 
-   329          2    -18.67517238    -18.864936      0.09488180756   4.972820174e-16 0               1.896631e-16    
+   329          2    64              -18.67254286    -18.864936      0.09619657243   8.881784197e-16 0               2.960594732e-16 
-   330          2    -17.53439276    -17.813086      0.1393466189    8.350923499e-16 0               3.215020842e-16 
+   330          2    68.921          -17.54726713    -17.813086      0.1329094363    1.371024298e-15 0               4.440892099e-16 
-   331          2    -11.04889659    -11.197201      0.07415220345   1.822150476e-14 0               6.092637968e-15 
+   331          2    19.683          -11.12327165    -11.197201      0.03696467615   4.343228798e-14 0               1.539509261e-14 
-   332          2    -23.68489671    -23.696705      0.00590414498   1.240124986e-15 0               4.153217122e-16 
+   332          2    35.937          -23.68985458    -23.696705      0.003425208911  8.588276581e-15 0               2.812564996e-15 
 # Volume_FCC.xyz
-  config   # atoms      energy        DFT energy     energy error     force          DFT force       force error
+  config   # atoms       volume        energy        DFT energy     energy error     force          DFT force       force error
-   333          4    -19.13390887    -19.075994      0.01447871809   1.022152812e-14 0               2.293587909e-15 
+   333          4    39.304          -19.04121551    -19.075994      0.008694621404  9.324046941e-14 0               2.550216982e-14 
-   334          4    -35.26038882    -34.873619      0.0966924543    1.299038035e-15 0               3.09937261e-16  
+   334          4    140.608         -35.2532829     -34.873619      0.09491597439   7.957989483e-17 0               1.134599845e-17 
-   335          4    -43.93272346    -43.950003      0.004319884816  1.839067075e-15 0               3.483902981e-16 
+   335          4    97.336          -43.90903851    -43.950003      0.01024112333   9.677895068e-15 0               2.24135791e-15  
-   336          4    -41.03733831    -40.991909      0.01135732773   4.481141716e-15 0               9.930207698e-16 
+   336          4    54.872          -41.05446227    -40.991909      0.01563831765   1.98280496e-14  0               4.875440329e-15 
-   337          4    -43.4228254     -43.453929      0.007775899668  3.563251054e-14 0               1.025252039e-14 
+   337          4    59.319          -43.40999789    -43.453929      0.01098277702   9.570074295e-14 0               2.719164593e-14 
-   338          4    -42.67289278    -42.686077      0.003296053998  3.08362874e-15  0               8.245357522e-16 
+   338          4    103.823         -42.63532355    -42.686077      0.01268836179   2.539930576e-15 0               4.806204543e-16 
-   339          4    -33.58842759    -33.224653      0.09094364633   7.806891681e-16 0               2.054201716e-16 
+   339          4    148.877         -33.58964546    -33.224653      0.09124811554   2.796923066e-17 0               3.296205444e-18 
-   340          4    -27.01189372    -26.862709      0.03729618105   6.429823751e-15 0               1.469359846e-15 
+   340          4    42.875          -26.8499756     -26.862709      0.003183350784  4.824942051e-14 0               1.148213469e-14 
-   341          4    -25.59030438    -25.519883      0.01760534598   1.262126674e-15 0               3.031429274e-16 
+   341          4    195.112         -25.5782856     -25.519883      0.01460065124   2.683808864e-16 0               5.477307421e-17 
-   342          4    3.441093749     3.463071        0.005494312714  2.222300041e-14 0               5.686075706e-15 
+   342          4    32.768          3.274215348     3.463071        0.04721391298   1.751484723e-13 0               4.608697683e-14 
-   343          4    -31.9073245     -31.59595       0.07784362479   8.772505365e-16 0               2.178523565e-16 
+   343          4    157.464         -31.91218763    -31.59595       0.07905940659   3.590442267e-17 0               4.231376791e-18 
-   344          4    -45.06068744    -45.100466      0.009944641012  2.844345405e-15 0               6.141228113e-16 
+   344          4    64              -45.05473725    -45.100466      0.01143218825   7.235555613e-15 0               1.620123306e-15 
-   345          4    -46.03981427    -46.052258      0.0031109323    3.085311895e-15 0               7.534482297e-16 
+   345          4    68.921          -46.04331302    -46.052258      0.002236244179  5.893206675e-15 0               1.299708229e-15 
-   346          4    -30.24326213    -30.001189      0.06051828302   1.033301257e-15 0               2.648344507e-16 
+   346          4    166.375         -30.2468098     -30.001189      0.06140519937   2.820758891e-16 0               5.580616674e-17 
-   347          4    -22.957351      -22.8504        0.02673775024   1.649470508e-15 0               4.625206468e-16 
+   347          4    216             -22.95485577    -22.8504        0.02611394167   1.164554524e-16 0               2.312964635e-17 
-   348          4    -9.130654755    -9.164691       0.008509061334  1.441769296e-14 0               2.967949237e-15 
+   348          4    35.937          -9.215415964    -9.164691       0.01268124103   4.893101434e-14 0               1.156092005e-14 
-   349          4    -24.21746226    -24.150343      0.01677981454   9.080179666e-16 0               2.344767898e-16 
+   349          4    205.379         -24.20645978    -24.150343      0.01402919404   2.781506505e-18 0               3.278036852e-19 
-   350          4    -46.44761241    -46.426795      0.005204351765  1.356833237e-15 0               3.249715312e-16 
+   350          4    74.088          -46.44951294    -46.426795      0.005679484598  2.411816735e-15 0               4.763070257e-16 
-   351          4    -28.62111495    -28.451145      0.04249248833   8.73448718e-15  0               2.511662753e-15 
+   351          4    175.616         -28.61960857    -28.451145      0.04211589328   1.078338842e-14 0               3.09506759e-15  
-   352          4    40.31615798     40.341566       0.006352005142  4.072809775e-14 0               8.11641299e-15  
+   352          4    27              40.45415396     40.341566       0.02814698887   1.556900619e-13 0               3.789568123e-14 
-   353          4    19.51151427     19.617912       0.02659943252   2.395447746e-14 0               5.536534686e-15 
+   353          4    29.791          19.42166568     19.617912       0.04906157941   1.398773649e-13 0               3.335786504e-14 
-   354          4    -27.06356399    -26.954384      0.02729499736   7.989451601e-16 0               1.662443331e-16 
+   354          4    185.193         -27.05578105    -26.954384      0.02534926276   2.758936733e-16 0               5.630535877e-17 
-   355          4    -46.3678929     -46.323696      0.01104922394   3.225354336e-15 0               8.604228441e-16 
+   355          4    79.507          -46.36425384    -46.323696      0.01013945879   2.152124725e-15 0               4.437884935e-16 
-   356          4    -45.87221055    -45.828947      0.01081588677   3.654195723e-15 0               9.691321819e-16 
+   356          4    85.184          -45.86352273    -45.828947      0.008643933117  3.448840532e-14 0               9.539924949e-15 
-   357          4    -38.47076405    -38.16029       0.0776185126    1.743572283e-15 0               4.628820475e-16 
+   357          4    125             -38.44027502    -38.16029       0.06999625463   1.884407826e-15 0               4.44194105e-16  
-   358          4    -33.06813795    -32.919741      0.03709923634   1.476523661e-14 0               4.182418301e-15 
+   358          4    46.656          -32.97168631    -32.919741      0.01298632653   1.142146022e-13 0               2.894877625e-14 
-   359          4    -41.34431995    -41.272675      0.01791123821   3.354385367e-15 0               9.014870014e-16 
+   359          4    110.592         -41.29864314    -41.272675      0.006492033936  3.342024128e-14 0               9.358862094e-15 
-   360          4    -39.95757678    -39.753322      0.05106369446   1.803308855e-15 0               4.257287097e-16 
+   360          4    117.649         -39.91686354    -39.753322      0.04088538603   7.303704341e-15 0               1.704201263e-15 
-   361          4    -37.66252943    -37.547435      0.02877360828   4.901403086e-15 0               1.0480621e-15   
+   361          4    50.653          -37.65718147    -37.547435      0.02743661628   2.105764443e-14 0               5.292352205e-15 
-   362          4    -36.89659259    -36.52595       0.09266064636   2.659569984e-15 0               6.744460314e-16 
+   362          4    132.651         -36.87810682    -36.52595       0.08803920465   3.379802923e-17 0               3.983135944e-18 
-   363          4    -45.03250721    -45.016087      0.004105053075  1.580168365e-15 0               3.385601984e-16 
+   363          4    91.125          -45.01844387    -45.016087      0.0005892174087 1.081458604e-14 0               2.513809578e-15 

examples/PACKAGES/pod/Ta/Ta_training_errors.pod

@@ -2,19 +2,19 @@
 ---------------------------------------------------------------------------------------------------
         File         | # configs |  # atoms  | MAE energy  | RMSE energy | MAE force  | RMSE force
 ---------------------------------------------------------------------------------------------------
-Displaced_A15.xyz            9         576     0.011286      0.011334      0.113353      0.141650  
+Displaced_A15.xyz            9         576     0.015324      0.015365      0.140594      0.184797  
-Displaced_BCC.xyz            9         486     0.012178      0.014005      0.240613      0.312191  
+Displaced_BCC.xyz            9         486     0.009486      0.011643      0.249983      0.320375  
-Displaced_FCC.xyz            9         432     0.001445      0.001591      0.082688      0.103800  
+Displaced_FCC.xyz            9         432     0.000686      0.000880      0.091420      0.113585  
-Elastic_BCC.xyz            100         200     0.004452      0.004783      0.000010      0.000013  
+Elastic_BCC.xyz            100         200     0.003796      0.004379      0.000015      0.000020  
-Elastic_FCC.xyz            100         400     0.002865      0.002923      0.000146      0.000207  
+Elastic_FCC.xyz            100         400     0.003332      0.003372      0.000122      0.000178  
-GSF_110.xyz                 22         528     0.005804      0.006853      0.047276      0.097819  
+GSF_110.xyz                 22         528     0.007027      0.007797      0.057637      0.115638  
-GSF_112.xyz                 22         660     0.010588      0.011555      0.123342      0.191090  
+GSF_112.xyz                 22         660     0.010396      0.011347      0.125237      0.198553  
-Liquid.xyz                   3         300     0.013161      0.015355      0.567536      0.757847  
+Liquid.xyz                   3         300     0.017584      0.023822      0.504354      0.660300  
-Surface.xyz                  7         236     0.025400      0.037555      0.096121      0.295623  
+Surface.xyz                  7         236     0.025511      0.034302      0.107190      0.285034  
-Volume_A15.xyz              30         240     0.039281      0.048678      0.000000      0.000000  
+Volume_A15.xyz              30         240     0.038624      0.048355      0.000000      0.000000  
-Volume_BCC.xyz              21          42     0.049766      0.067554      0.000000      0.000000  
+Volume_BCC.xyz              21          42     0.044423      0.061685      0.000000      0.000000  
-Volume_FCC.xyz              31         124     0.030056      0.041738      0.000000      0.000000  
+Volume_FCC.xyz              31         124     0.030062      0.041271      0.000000      0.000000  
 ---------------------------------------------------------------------------------------------------
-All files                  363        4224     0.012917      0.025797      0.122473      0.260052  
+All files                  363        4224     0.012618      0.024806      0.125879      0.247229  
 ---------------------------------------------------------------------------------------------------
 **************** End of Error Analysis for the Training Data Set ****************

examples/PACKAGES/pod/Ta/in.fitpod

@@ -1,5 +1 @@
-# Demonstrate fitpod for POD potential
+fitpod Ta_param.pod Ta_data.pod
-
-units metal
-fitpod Ta_param.pod Ta_data.pod
-

examples/PACKAGES/pod/Ta/in.pod

@@ -44,4 +44,3 @@ velocity all create 300.0 4928459 loop geom
 fix 1 all nve
 run             ${nsteps}
 
-

examples/PACKAGES/pod/Ta/in.pod.compute

@@ -0,0 +1,52 @@
+# Demonstrate bispectrum computes
+
+# initialize simulation
+
+variable 	nsteps index 0
+variable 	nrep equal 2
+variable 	a equal 2.0
+units		metal
+
+# generate the box and atom positions using a BCC lattice
+
+variable 	nx equal ${nrep}
+variable 	ny equal ${nrep}
+variable 	nz equal ${nrep}
+
+boundary	p p p
+
+atom_modify	map hash
+lattice         bcc $a
+region		box block 0 ${nx} 0 ${ny} 0 ${nz}
+create_box	2 box
+create_atoms	2 box
+
+mass 		* 180.88
+
+displace_atoms 	all random 0.1 0.1 0.1 123456
+
+# set up dummy potential to satisfy cutoff
+variable 	rcutfac equal 6.0
+pair_style 	zero ${rcutfac}
+pair_coeff 	* *
+
+# set up per-atom computes
+
+compute ld all pod/atom Ta_param.pod Ta_coefficients.pod Ta Ta
+compute dd all podd/atom Ta_param.pod Ta_coefficients.pod Ta Ta
+
+# set up compute snap generating global array
+
+compute gdd all pod/global Ta_param.pod Ta_coefficients.pod Ta Ta
+#fix 		gdd all ave/time 1 1 1 c_gdd[*] file pod.gdd.dat mode vector
+
+compute ldd all pod/local Ta_param.pod Ta_coefficients.pod Ta Ta
+#fix 		ldd all ave/time 1 1 1 c_ldd[*] file pod.ldd.dat mode vector
+
+#dump 		mydump_ld all custom 1000 dump_ld id c_ld[*]
+#dump 		mydump_dd all custom 1000 dump_dd id c_dd[*]
+
+variable sample_ld1 equal C_ld[1][10]  # Arbitrary local descriptor
+fix ldprint all print 1 "${sample_ld1}" 
+
+run             ${nsteps}

examples/PACKAGES/pod/Ta/log.22May24.fitpod.g++.1

@@ -1,32 +1,37 @@
-LAMMPS (22 Dec 2022)
+LAMMPS (17 Apr 2024 - Development - patch_17Apr2024-177-g86abf4f680-modified)
+OMP_NUM_THREADS environment is not set. Defaulting to 1 thread. (src/comm.cpp:98)
   using 1 OpenMP thread(s) per MPI task
-# Demonstrate fitpod for POD potential
-
-units metal
 fitpod Ta_param.pod Ta_data.pod
-Reading potential file Ta_param.pod with DATE: 2022-11-30
 **************** Begin of POD Potentials ****************
 species: Ta 
 periodic boundary conditions: 1 1 1
+number of environment clusters: 1
+number of principal compoments: 2
 inner cut-off radius: 1
 outer cut-off radius: 5
 bessel polynomial degree: 3
 inverse polynomial degree: 6
 one-body potential: 1
-two-body potential: 3 6 6
+two-body radial basis functions: 6
-three-body potential: 3 6 5 5
+three-body radial basis functions: 5
-four-body SNAP potential: 0 0
+three-body angular degree: 4
-quadratic POD potential: 0
+four-body radial basis functions: 0
-number of basis functions for one-body potential: 1
+four-body angular degree: 0
-number of basis functions for two-body potential: 6
+five-body radial basis functions: 0
-number of basis functions for three-body potential: 25
+five-body angular degree: 0
-number of basis functions for four-body potential: 0
+six-body radial basis functions: 0
-number of descriptors for one-body potential: 1
+six-body angular degree: 0
-number of descriptors for two-body potential: 6
+seven-body radial basis functions: 0
-number of descriptors for three-body potential: 25
+seven-body angular degree: 0
-number of descriptors for four-body potential: 0
+number of local descriptors per element for one-body potential: 1
-number of descriptors for quadratic POD potential: 0
+number of local descriptors per element for two-body potential: 6
-total number of descriptors for all potentials: 32
+number of local descriptors per element for three-body potential: 25
+number of local descriptors per element for four-body potential: 0
+number of local descriptors per element for five-body potential: 0
+number of local descriptors per element for six-body potential: 0
+number of local descriptors per element for seven-body potential: 0
+number of local descriptors per element for all potentials: 32
+number of global descriptors: 32
 **************** End of POD Potentials ****************
 
 **************** Begin of Data File ****************
@@ -34,6 +39,8 @@ file format: extxyz
 file extension: xyz
 path to training data set: XYZ
 path to test data set: XYZ
+path to environment configuration set: XYZ
+basename for output files: Ta
 training fraction: 1
 test fraction: 1
 randomize training data set: 1
@@ -45,7 +52,8 @@ energy/force calculation for test data set: 0
 fitting weight for energy: 100
 fitting weight for force: 1
 fitting weight for stress: 0
-fitting regularization parameter: 1e-10
+save pod descriptors: 0
+compute pod descriptors: 0
 **************** End of Data File ****************
 **************** Begin of Training Data Set ****************
 ---------------------------------------------------------------
@@ -74,8 +82,7 @@ maximum number of atoms: 100
 maximum number of atoms in periodic domain: 100
 maximum number of atoms in extended domain: 2700
 maximum number of neighbors in extended domain: 270000
-size of double memory: 223201
+size of double memory: 232128
-size of int memory: 14709
 size of descriptor matrix: 32 x 32
 **************** End of Memory Allocation ****************
 **************** Begin of Least-Squares Fitting ****************
@@ -83,7 +90,6 @@ Configuration: # 1
 Configuration: # 101
 Configuration: # 201
 Configuration: # 301
-**************** End of Least-Squares Fitting ****************
 **************** Begin of Error Calculation ****************
 Configuration: # 1
 Configuration: # 101
@@ -94,21 +100,20 @@ Configuration: # 301
 ---------------------------------------------------------------------------------------------------
         File         | # configs |  # atoms  | MAE energy  | RMSE energy | MAE force  | RMSE force
 ---------------------------------------------------------------------------------------------------
-Displaced_A15.xyz            9         576     0.011286      0.011334      0.113353      0.141650  
+Displaced_A15.xyz            9         576     0.015324      0.015365      0.140594      0.184797  
-Displaced_BCC.xyz            9         486     0.012178      0.014005      0.240613      0.312191  
+Displaced_BCC.xyz            9         486     0.009486      0.011643      0.249983      0.320375  
-Displaced_FCC.xyz            9         432     0.001445      0.001591      0.082688      0.103800  
+Displaced_FCC.xyz            9         432     0.000686      0.000880      0.091420      0.113585  
-Elastic_BCC.xyz            100         200     0.004452      0.004783      0.000010      0.000013  
+Elastic_BCC.xyz            100         200     0.003796      0.004379      0.000015      0.000020  
-Elastic_FCC.xyz            100         400     0.002865      0.002923      0.000146      0.000207  
+Elastic_FCC.xyz            100         400     0.003332      0.003372      0.000122      0.000178  
-GSF_110.xyz                 22         528     0.005804      0.006853      0.047276      0.097819  
+GSF_110.xyz                 22         528     0.007027      0.007797      0.057637      0.115638  
-GSF_112.xyz                 22         660     0.010588      0.011555      0.123342      0.191090  
+GSF_112.xyz                 22         660     0.010396      0.011347      0.125237      0.198553  
-Liquid.xyz                   3         300     0.013161      0.015355      0.567536      0.757847  
+Liquid.xyz                   3         300     0.017584      0.023822      0.504354      0.660300  
-Surface.xyz                  7         236     0.025400      0.037555      0.096121      0.295623  
+Surface.xyz                  7         236     0.025511      0.034302      0.107190      0.285034  
-Volume_A15.xyz              30         240     0.039281      0.048678      0.000000      0.000000  
+Volume_A15.xyz              30         240     0.038624      0.048355      0.000000      0.000000  
-Volume_BCC.xyz              21          42     0.049766      0.067554      0.000000      0.000000  
+Volume_BCC.xyz              21          42     0.044423      0.061685      0.000000      0.000000  
-Volume_FCC.xyz              31         124     0.030056      0.041738      0.000000      0.000000  
+Volume_FCC.xyz              31         124     0.030062      0.041271      0.000000      0.000000  
 ---------------------------------------------------------------------------------------------------
-All files                  363        4224     0.012917      0.025797      0.122473      0.260052  
+All files                  363        4224     0.012618      0.024806      0.125879      0.247229  
 ---------------------------------------------------------------------------------------------------
 **************** End of Error Analysis for the Training Data Set ****************
-
 Total wall time: 0:00:00

examples/PACKAGES/pod/Ta/log.22May24.fitpod.g++.4

@@ -1,32 +1,37 @@
-LAMMPS (22 Dec 2022)
+LAMMPS (17 Apr 2024 - Development - patch_17Apr2024-177-g86abf4f680-modified)
+OMP_NUM_THREADS environment is not set. Defaulting to 1 thread. (src/comm.cpp:98)
   using 1 OpenMP thread(s) per MPI task
-# Demonstrate fitpod for POD potential
-
-units metal
 fitpod Ta_param.pod Ta_data.pod
-Reading potential file Ta_param.pod with DATE: 2022-11-30
 **************** Begin of POD Potentials ****************
 species: Ta 
 periodic boundary conditions: 1 1 1
+number of environment clusters: 1
+number of principal compoments: 2
 inner cut-off radius: 1
 outer cut-off radius: 5
 bessel polynomial degree: 3
 inverse polynomial degree: 6
 one-body potential: 1
-two-body potential: 3 6 6
+two-body radial basis functions: 6
-three-body potential: 3 6 5 5
+three-body radial basis functions: 5
-four-body SNAP potential: 0 0
+three-body angular degree: 4
-quadratic POD potential: 0
+four-body radial basis functions: 0
-number of basis functions for one-body potential: 1
+four-body angular degree: 0
-number of basis functions for two-body potential: 6
+five-body radial basis functions: 0
-number of basis functions for three-body potential: 25
+five-body angular degree: 0
-number of basis functions for four-body potential: 0
+six-body radial basis functions: 0
-number of descriptors for one-body potential: 1
+six-body angular degree: 0
-number of descriptors for two-body potential: 6
+seven-body radial basis functions: 0
-number of descriptors for three-body potential: 25
+seven-body angular degree: 0
-number of descriptors for four-body potential: 0
+number of local descriptors per element for one-body potential: 1
-number of descriptors for quadratic POD potential: 0
+number of local descriptors per element for two-body potential: 6
-total number of descriptors for all potentials: 32
+number of local descriptors per element for three-body potential: 25
+number of local descriptors per element for four-body potential: 0
+number of local descriptors per element for five-body potential: 0
+number of local descriptors per element for six-body potential: 0
+number of local descriptors per element for seven-body potential: 0
+number of local descriptors per element for all potentials: 32
+number of global descriptors: 32
 **************** End of POD Potentials ****************
 
 **************** Begin of Data File ****************
@@ -34,6 +39,8 @@ file format: extxyz
 file extension: xyz
 path to training data set: XYZ
 path to test data set: XYZ
+path to environment configuration set: XYZ
+basename for output files: Ta
 training fraction: 1
 test fraction: 1
 randomize training data set: 1
@@ -45,7 +52,8 @@ energy/force calculation for test data set: 0
 fitting weight for energy: 100
 fitting weight for force: 1
 fitting weight for stress: 0
-fitting regularization parameter: 1e-10
+save pod descriptors: 0
+compute pod descriptors: 0
 **************** End of Data File ****************
 **************** Begin of Training Data Set ****************
 ---------------------------------------------------------------
@@ -74,8 +82,7 @@ maximum number of atoms: 100
 maximum number of atoms in periodic domain: 100
 maximum number of atoms in extended domain: 2700
 maximum number of neighbors in extended domain: 270000
-size of double memory: 223201
+size of double memory: 232128
-size of int memory: 14709
 size of descriptor matrix: 32 x 32
 **************** End of Memory Allocation ****************
 **************** Begin of Least-Squares Fitting ****************
@@ -83,7 +90,6 @@ Configuration: # 1
 Configuration: # 101
 Configuration: # 201
 Configuration: # 301
-**************** End of Least-Squares Fitting ****************
 **************** Begin of Error Calculation ****************
 Configuration: # 1
 Configuration: # 101
@@ -94,21 +100,20 @@ Configuration: # 301
 ---------------------------------------------------------------------------------------------------
         File         | # configs |  # atoms  | MAE energy  | RMSE energy | MAE force  | RMSE force
 ---------------------------------------------------------------------------------------------------
-Displaced_A15.xyz            9         576     0.011286      0.011334      0.113353      0.141650  
+Displaced_A15.xyz            9         576     0.015324      0.015365      0.140594      0.184797  
-Displaced_BCC.xyz            9         486     0.012178      0.014005      0.240613      0.312191  
+Displaced_BCC.xyz            9         486     0.009486      0.011643      0.249983      0.320375  
-Displaced_FCC.xyz            9         432     0.001445      0.001591      0.082688      0.103800  
+Displaced_FCC.xyz            9         432     0.000686      0.000880      0.091420      0.113585  
-Elastic_BCC.xyz            100         200     0.004452      0.004783      0.000010      0.000013  
+Elastic_BCC.xyz            100         200     0.003796      0.004379      0.000015      0.000020  
-Elastic_FCC.xyz            100         400     0.002865      0.002923      0.000146      0.000207  
+Elastic_FCC.xyz            100         400     0.003332      0.003372      0.000122      0.000178  
-GSF_110.xyz                 22         528     0.005804      0.006853      0.047276      0.097819  
+GSF_110.xyz                 22         528     0.007027      0.007797      0.057637      0.115638  
-GSF_112.xyz                 22         660     0.010588      0.011555      0.123342      0.191090  
+GSF_112.xyz                 22         660     0.010396      0.011347      0.125237      0.198553  
-Liquid.xyz                   3         300     0.013161      0.015355      0.567536      0.757847  
+Liquid.xyz                   3         300     0.017584      0.023822      0.504354      0.660300  
-Surface.xyz                  7         236     0.025400      0.037555      0.096121      0.295623  
+Surface.xyz                  7         236     0.025511      0.034302      0.107190      0.285034  
-Volume_A15.xyz              30         240     0.039281      0.048678      0.000000      0.000000  
+Volume_A15.xyz              30         240     0.038624      0.048355      0.000000      0.000000  
-Volume_BCC.xyz              21          42     0.049766      0.067554      0.000000      0.000000  
+Volume_BCC.xyz              21          42     0.044423      0.061685      0.000000      0.000000  
-Volume_FCC.xyz              31         124     0.030056      0.041738      0.000000      0.000000  
+Volume_FCC.xyz              31         124     0.030062      0.041271      0.000000      0.000000  
 ---------------------------------------------------------------------------------------------------
-All files                  363        4224     0.012917      0.025797      0.122473      0.260052  
+All files                  363        4224     0.012618      0.024806      0.125879      0.247229  
 ---------------------------------------------------------------------------------------------------
 **************** End of Error Analysis for the Training Data Set ****************
-
+Total wall time: 0:00:00
-Total wall time: 0:00:01

examples/PACKAGES/pod/Ta/log.22May24.pod.compute.g++.1

@@ -0,0 +1,293 @@
+LAMMPS (17 Apr 2024 - Development - patch_17Apr2024-177-g86abf4f680-modified)
+OMP_NUM_THREADS environment is not set. Defaulting to 1 thread. (src/comm.cpp:98)
+  using 1 OpenMP thread(s) per MPI task
+# Demonstrate bispectrum computes
+
+# initialize simulation
+
+variable 	nsteps index 0
+variable 	nrep equal 2
+variable 	a equal 2.0
+units		metal
+
+# generate the box and atom positions using a BCC lattice
+
+variable 	nx equal ${nrep}
+variable 	nx equal 2
+variable 	ny equal ${nrep}
+variable 	ny equal 2
+variable 	nz equal ${nrep}
+variable 	nz equal 2
+
+boundary	p p p
+
+atom_modify	map hash
+lattice         bcc $a
+lattice         bcc 2
+Lattice spacing in x,y,z = 2 2 2
+region		box block 0 ${nx} 0 ${ny} 0 ${nz}
+region		box block 0 2 0 ${ny} 0 ${nz}
+region		box block 0 2 0 2 0 ${nz}
+region		box block 0 2 0 2 0 2
+create_box	2 box
+Created orthogonal box = (0 0 0) to (4 4 4)
+  1 by 1 by 1 MPI processor grid
+create_atoms	2 box
+Created 16 atoms
+  using lattice units in orthogonal box = (0 0 0) to (4 4 4)
+  create_atoms CPU = 0.001 seconds
+
+mass 		* 180.88
+
+displace_atoms 	all random 0.1 0.1 0.1 123456
+Displacing atoms ...
+
+# set up dummy potential to satisfy cutoff
+variable 	rcutfac equal 6.0
+pair_style 	zero ${rcutfac}
+pair_style 	zero 6
+pair_coeff 	* *
+
+# set up per-atom computes
+
+compute ld all pod/atom Ta_param.pod Ta_coefficients.pod Ta Ta
+**************** Begin of POD Potentials ****************
+species: Ta 
+periodic boundary conditions: 1 1 1
+number of environment clusters: 1
+number of principal compoments: 2
+inner cut-off radius: 1
+outer cut-off radius: 5
+bessel polynomial degree: 3
+inverse polynomial degree: 6
+one-body potential: 1
+two-body radial basis functions: 6
+three-body radial basis functions: 5
+three-body angular degree: 4
+four-body radial basis functions: 0
+four-body angular degree: 0
+five-body radial basis functions: 0
+five-body angular degree: 0
+six-body radial basis functions: 0
+six-body angular degree: 0
+seven-body radial basis functions: 0
+seven-body angular degree: 0
+number of local descriptors per element for one-body potential: 1
+number of local descriptors per element for two-body potential: 6
+number of local descriptors per element for three-body potential: 25
+number of local descriptors per element for four-body potential: 0
+number of local descriptors per element for five-body potential: 0
+number of local descriptors per element for six-body potential: 0
+number of local descriptors per element for seven-body potential: 0
+number of local descriptors per element for all potentials: 32
+number of global descriptors: 32
+**************** End of POD Potentials ****************
+
+**************** Begin of Model Coefficients ****************
+total number of coefficients for POD potential: 32
+total number of elements for PCA projection matrix: 0
+total number of elements for PCA centroids: 0
+**************** End of Model Coefficients ****************
+
+compute dd all podd/atom Ta_param.pod Ta_coefficients.pod Ta Ta
+**************** Begin of POD Potentials ****************
+species: Ta 
+periodic boundary conditions: 1 1 1
+number of environment clusters: 1
+number of principal compoments: 2
+inner cut-off radius: 1
+outer cut-off radius: 5
+bessel polynomial degree: 3
+inverse polynomial degree: 6
+one-body potential: 1
+two-body radial basis functions: 6
+three-body radial basis functions: 5
+three-body angular degree: 4
+four-body radial basis functions: 0
+four-body angular degree: 0
+five-body radial basis functions: 0
+five-body angular degree: 0
+six-body radial basis functions: 0
+six-body angular degree: 0
+seven-body radial basis functions: 0
+seven-body angular degree: 0
+number of local descriptors per element for one-body potential: 1
+number of local descriptors per element for two-body potential: 6
+number of local descriptors per element for three-body potential: 25
+number of local descriptors per element for four-body potential: 0
+number of local descriptors per element for five-body potential: 0
+number of local descriptors per element for six-body potential: 0
+number of local descriptors per element for seven-body potential: 0
+number of local descriptors per element for all potentials: 32
+number of global descriptors: 32
+**************** End of POD Potentials ****************
+
+**************** Begin of Model Coefficients ****************
+total number of coefficients for POD potential: 32
+total number of elements for PCA projection matrix: 0
+total number of elements for PCA centroids: 0
+**************** End of Model Coefficients ****************
+
+
+# set up compute snap generating global array
+
+compute gdd all pod/gdd Ta_param.pod Ta_coefficients.pod Ta Ta
+**************** Begin of POD Potentials ****************
+species: Ta 
+periodic boundary conditions: 1 1 1
+number of environment clusters: 1
+number of principal compoments: 2
+inner cut-off radius: 1
+outer cut-off radius: 5
+bessel polynomial degree: 3
+inverse polynomial degree: 6
+one-body potential: 1
+two-body radial basis functions: 6
+three-body radial basis functions: 5
+three-body angular degree: 4
+four-body radial basis functions: 0
+four-body angular degree: 0
+five-body radial basis functions: 0
+five-body angular degree: 0
+six-body radial basis functions: 0
+six-body angular degree: 0
+seven-body radial basis functions: 0
+seven-body angular degree: 0
+number of local descriptors per element for one-body potential: 1
+number of local descriptors per element for two-body potential: 6
+number of local descriptors per element for three-body potential: 25
+number of local descriptors per element for four-body potential: 0
+number of local descriptors per element for five-body potential: 0
+number of local descriptors per element for six-body potential: 0
+number of local descriptors per element for seven-body potential: 0
+number of local descriptors per element for all potentials: 32
+number of global descriptors: 32
+**************** End of POD Potentials ****************
+
+**************** Begin of Model Coefficients ****************
+total number of coefficients for POD potential: 32
+total number of elements for PCA projection matrix: 0
+total number of elements for PCA centroids: 0
+**************** End of Model Coefficients ****************
+
+#fix 		gdd all ave/time 1 1 1 c_gdd[*] file pod.gdd.dat mode vector
+
+compute ldd all pod/ldd Ta_param.pod Ta_coefficients.pod Ta Ta
+**************** Begin of POD Potentials ****************
+species: Ta 
+periodic boundary conditions: 1 1 1
+number of environment clusters: 1
+number of principal compoments: 2
+inner cut-off radius: 1
+outer cut-off radius: 5
+bessel polynomial degree: 3
+inverse polynomial degree: 6
+one-body potential: 1
+two-body radial basis functions: 6
+three-body radial basis functions: 5
+three-body angular degree: 4
+four-body radial basis functions: 0
+four-body angular degree: 0
+five-body radial basis functions: 0
+five-body angular degree: 0
+six-body radial basis functions: 0
+six-body angular degree: 0
+seven-body radial basis functions: 0
+seven-body angular degree: 0
+number of local descriptors per element for one-body potential: 1
+number of local descriptors per element for two-body potential: 6
+number of local descriptors per element for three-body potential: 25
+number of local descriptors per element for four-body potential: 0
+number of local descriptors per element for five-body potential: 0
+number of local descriptors per element for six-body potential: 0
+number of local descriptors per element for seven-body potential: 0
+number of local descriptors per element for all potentials: 32
+number of global descriptors: 32
+**************** End of POD Potentials ****************
+
+**************** Begin of Model Coefficients ****************
+total number of coefficients for POD potential: 32
+total number of elements for PCA projection matrix: 0
+total number of elements for PCA centroids: 0
+**************** End of Model Coefficients ****************
+
+#fix 		ldd all ave/time 1 1 1 c_ldd[*] file pod.ldd.dat mode vector
+
+#dump 		mydump_ld all custom 1000 dump_ld id c_ld[*]
+#dump 		mydump_dd all custom 1000 dump_dd id c_dd[*]
+
+variable sample_ld1 equal C_ld[1][10]  # Arbitrary local descriptor
+fix ldprint all print 1 "${sample_ld1}"
+
+run             ${nsteps}
+run             0
+WARNING: No fixes with time integration, atoms won't move (src/verlet.cpp:60)
+Generated 0 of 1 mixed pair_coeff terms from geometric mixing rule
+WARNING: More than one compute pod (src/ML-POD/compute_pod_atom.cpp:87)
+WARNING: More than one compute pod (src/ML-POD/compute_podd_atom.cpp:87)
+WARNING: More than one compute pod (src/ML-POD/compute_pod_global.cpp:87)
+WARNING: More than one compute pod (src/ML-POD/compute_pod_local.cpp:89)
+Neighbor list info ...
+  update: every = 1 steps, delay = 0 steps, check = yes
+  max neighbors/atom: 2000, page size: 100000
+  master list distance cutoff = 8
+  ghost atom cutoff = 8
+  binsize = 4, bins = 1 1 1
+  5 neighbor lists, perpetual/occasional/extra = 1 4 0
+  (1) pair zero, perpetual
+      attributes: half, newton on
+      pair build: half/bin/atomonly/newton
+      stencil: half/bin/3d
+      bin: standard
+  (2) compute pod/atom, occasional
+      attributes: full, newton on
+      pair build: full/bin/atomonly
+      stencil: full/bin/3d
+      bin: standard
+  (3) compute podd/atom, occasional
+      attributes: full, newton on
+      pair build: full/bin/atomonly
+      stencil: full/bin/3d
+      bin: standard
+  (4) compute pod/gdd, occasional
+      attributes: full, newton on
+      pair build: full/bin/atomonly
+      stencil: full/bin/3d
+      bin: standard
+  (5) compute pod/ldd, occasional
+      attributes: full, newton on
+      pair build: full/bin/atomonly
+      stencil: full/bin/3d
+      bin: standard
+0.344594831165384
+Per MPI rank memory allocation (min/avg/max) = 6.326 | 6.326 | 6.326 Mbytes
+   Step          Temp          E_pair         E_mol          TotEng         Press     
+         0   0              0              0              0              0            
+Loop time of 1.207e-06 on 1 procs for 0 steps with 16 atoms
+
+165.7% CPU use with 1 MPI tasks x 1 OpenMP threads
+
+MPI task timing breakdown:
+Section |  min time  |  avg time  |  max time  |%varavg| %total
+---------------------------------------------------------------
+Pair    | 0          | 0          | 0          |   0.0 |  0.00
+Neigh   | 0          | 0          | 0          |   0.0 |  0.00
+Comm    | 0          | 0          | 0          |   0.0 |  0.00
+Output  | 0          | 0          | 0          |   0.0 |  0.00
+Modify  | 0          | 0          | 0          |   0.0 |  0.00
+Other   |            | 1.207e-06  |            |       |100.00
+
+Nlocal:             16 ave          16 max          16 min
+Histogram: 1 0 0 0 0 0 0 0 0 0
+Nghost:           1984 ave        1984 max        1984 min
+Histogram: 1 0 0 0 0 0 0 0 0 0
+Neighs:           4311 ave        4311 max        4311 min
+Histogram: 1 0 0 0 0 0 0 0 0 0
+FullNghs:         8623 ave        8623 max        8623 min
+Histogram: 1 0 0 0 0 0 0 0 0 0
+
+Total # of neighbors = 8623
+Ave neighs/atom = 538.9375
+Neighbor list builds = 0
+Dangerous builds = 0
+Total wall time: 0:00:00

examples/PACKAGES/pod/Ta/log.22May24.pod.g++.1

@@ -0,0 +1,155 @@
+LAMMPS (17 Apr 2024 - Development - patch_17Apr2024-177-g86abf4f680-modified)
+OMP_NUM_THREADS environment is not set. Defaulting to 1 thread. (src/comm.cpp:98)
+  using 1 OpenMP thread(s) per MPI task
+# Demonstrate POD Ta potential
+
+# Initialize simulation
+
+variable nsteps index 100
+variable nrep equal 4
+variable a equal 3.316
+units           metal
+
+# generate the box and atom positions using a BCC lattice
+
+variable nx equal ${nrep}
+variable nx equal 4
+variable ny equal ${nrep}
+variable ny equal 4
+variable nz equal ${nrep}
+variable nz equal 4
+
+boundary        p p p
+
+lattice         bcc $a
+lattice         bcc 3.316
+Lattice spacing in x,y,z = 3.316 3.316 3.316
+region          box block 0 ${nx} 0 ${ny} 0 ${nz}
+region          box block 0 4 0 ${ny} 0 ${nz}
+region          box block 0 4 0 4 0 ${nz}
+region          box block 0 4 0 4 0 4
+create_box      1 box
+Created orthogonal box = (0 0 0) to (13.264 13.264 13.264)
+  1 by 1 by 1 MPI processor grid
+create_atoms    1 box
+Created 128 atoms
+  using lattice units in orthogonal box = (0 0 0) to (13.264 13.264 13.264)
+  create_atoms CPU = 0.001 seconds
+
+mass 1 180.88
+
+
+# POD potential
+pair_style pod
+pair_coeff * * Ta_param.pod Ta_coeff.pod Ta
+**************** Begin of POD Potentials ****************
+species: Ta 
+periodic boundary conditions: 1 1 1
+number of environment clusters: 1
+number of principal compoments: 2
+inner cut-off radius: 1
+outer cut-off radius: 5
+bessel polynomial degree: 3
+inverse polynomial degree: 6
+one-body potential: 1
+two-body radial basis functions: 6
+three-body radial basis functions: 5
+three-body angular degree: 4
+four-body radial basis functions: 0
+four-body angular degree: 0
+five-body radial basis functions: 0
+five-body angular degree: 0
+six-body radial basis functions: 0
+six-body angular degree: 0
+seven-body radial basis functions: 0
+seven-body angular degree: 0
+number of local descriptors per element for one-body potential: 1
+number of local descriptors per element for two-body potential: 6
+number of local descriptors per element for three-body potential: 25
+number of local descriptors per element for four-body potential: 0
+number of local descriptors per element for five-body potential: 0
+number of local descriptors per element for six-body potential: 0
+number of local descriptors per element for seven-body potential: 0
+number of local descriptors per element for all potentials: 32
+number of global descriptors: 32
+**************** End of POD Potentials ****************
+
+**************** Begin of Model Coefficients ****************
+total number of coefficients for POD potential: 32
+total number of elements for PCA projection matrix: 0
+total number of elements for PCA centroids: 0
+**************** End of Model Coefficients ****************
+
+
+# Setup output
+
+thermo          10
+thermo_modify norm yes
+
+# Set up NVE run
+
+timestep 0.5e-3
+neighbor 1.0 bin
+neigh_modify once no every 1 delay 0 check yes
+
+# Run MD
+
+velocity all create 300.0 4928459 loop geom
+fix 1 all nve
+run             ${nsteps}
+run             100
+Neighbor list info ...
+  update: every = 1 steps, delay = 0 steps, check = yes
+  max neighbors/atom: 2000, page size: 100000
+  master list distance cutoff = 6
+  ghost atom cutoff = 6
+  binsize = 3, bins = 5 5 5
+  1 neighbor lists, perpetual/occasional/extra = 1 0 0
+  (1) pair pod, perpetual
+      attributes: full, newton on
+      pair build: full/bin/atomonly
+      stencil: full/bin/3d
+      bin: standard
+Per MPI rank memory allocation (min/avg/max) = 3.207 | 3.207 | 3.207 Mbytes
+   Step          Temp          E_pair         E_mol          TotEng         Press     
+         0   300           -11.842971      0             -11.804496     -24843.054    
+        10   296.87227     -11.84257       0             -11.804496     -24609.859    
+        20   287.65971     -11.841388      0             -11.804496     -23926.722    
+        30   272.87511     -11.839492      0             -11.804496     -22841.672    
+        40   253.34724     -11.836988      0             -11.804496     -21429.268    
+        50   230.17169     -11.834015      0             -11.804496     -19782.77     
+        60   204.64408     -11.830741      0             -11.804496     -18004.755    
+        70   178.17888     -11.827347      0             -11.804495     -16197.482    
+        80   152.21769     -11.824017      0             -11.804495     -14454.425    
+        90   128.13189     -11.820928      0             -11.804495     -12854.075    
+       100   107.12666     -11.818234      0             -11.804495     -11456.437    
+Loop time of 0.394952 on 1 procs for 100 steps with 128 atoms
+
+Performance: 10.938 ns/day, 2.194 hours/ns, 253.196 timesteps/s, 32.409 katom-step/s
+97.4% CPU use with 1 MPI tasks x 1 OpenMP threads
+
+MPI task timing breakdown:
+Section |  min time  |  avg time  |  max time  |%varavg| %total
+---------------------------------------------------------------
+Pair    | 0.39249    | 0.39249    | 0.39249    |   0.0 | 99.38
+Neigh   | 0          | 0          | 0          |   0.0 |  0.00
+Comm    | 0.00087496 | 0.00087496 | 0.00087496 |   0.0 |  0.22
+Output  | 0.00030885 | 0.00030885 | 0.00030885 |   0.0 |  0.08
+Modify  | 0.00053218 | 0.00053218 | 0.00053218 |   0.0 |  0.13
+Other   |            | 0.0007481  |            |       |  0.19
+
+Nlocal:            128 ave         128 max         128 min
+Histogram: 1 0 0 0 0 0 0 0 0 0
+Nghost:            727 ave         727 max         727 min
+Histogram: 1 0 0 0 0 0 0 0 0 0
+Neighs:              0 ave           0 max           0 min
+Histogram: 1 0 0 0 0 0 0 0 0 0
+FullNghs:         7424 ave        7424 max        7424 min
+Histogram: 1 0 0 0 0 0 0 0 0 0
+
+Total # of neighbors = 7424
+Ave neighs/atom = 58
+Neighbor list builds = 0
+Dangerous builds = 0
+
+Total wall time: 0:00:00

examples/PACKAGES/pod/Ta/log.22May24.pod.g++.4

@@ -0,0 +1,155 @@
+LAMMPS (17 Apr 2024 - Development - patch_17Apr2024-177-g86abf4f680-modified)
+OMP_NUM_THREADS environment is not set. Defaulting to 1 thread. (src/comm.cpp:98)
+  using 1 OpenMP thread(s) per MPI task
+# Demonstrate POD Ta potential
+
+# Initialize simulation
+
+variable nsteps index 100
+variable nrep equal 4
+variable a equal 3.316
+units           metal
+
+# generate the box and atom positions using a BCC lattice
+
+variable nx equal ${nrep}
+variable nx equal 4
+variable ny equal ${nrep}
+variable ny equal 4
+variable nz equal ${nrep}
+variable nz equal 4
+
+boundary        p p p
+
+lattice         bcc $a
+lattice         bcc 3.316
+Lattice spacing in x,y,z = 3.316 3.316 3.316
+region          box block 0 ${nx} 0 ${ny} 0 ${nz}
+region          box block 0 4 0 ${ny} 0 ${nz}
+region          box block 0 4 0 4 0 ${nz}
+region          box block 0 4 0 4 0 4
+create_box      1 box
+Created orthogonal box = (0 0 0) to (13.264 13.264 13.264)
+  1 by 2 by 2 MPI processor grid
+create_atoms    1 box
+Created 128 atoms
+  using lattice units in orthogonal box = (0 0 0) to (13.264 13.264 13.264)
+  create_atoms CPU = 0.001 seconds
+
+mass 1 180.88
+
+
+# POD potential
+pair_style pod
+pair_coeff * * Ta_param.pod Ta_coeff.pod Ta
+**************** Begin of POD Potentials ****************
+species: Ta 
+periodic boundary conditions: 1 1 1
+number of environment clusters: 1
+number of principal compoments: 2
+inner cut-off radius: 1
+outer cut-off radius: 5
+bessel polynomial degree: 3
+inverse polynomial degree: 6
+one-body potential: 1
+two-body radial basis functions: 6
+three-body radial basis functions: 5
+three-body angular degree: 4
+four-body radial basis functions: 0
+four-body angular degree: 0
+five-body radial basis functions: 0
+five-body angular degree: 0
+six-body radial basis functions: 0
+six-body angular degree: 0
+seven-body radial basis functions: 0
+seven-body angular degree: 0
+number of local descriptors per element for one-body potential: 1
+number of local descriptors per element for two-body potential: 6
+number of local descriptors per element for three-body potential: 25
+number of local descriptors per element for four-body potential: 0
+number of local descriptors per element for five-body potential: 0
+number of local descriptors per element for six-body potential: 0
+number of local descriptors per element for seven-body potential: 0
+number of local descriptors per element for all potentials: 32
+number of global descriptors: 32
+**************** End of POD Potentials ****************
+
+**************** Begin of Model Coefficients ****************
+total number of coefficients for POD potential: 32
+total number of elements for PCA projection matrix: 0
+total number of elements for PCA centroids: 0
+**************** End of Model Coefficients ****************
+
+
+# Setup output
+
+thermo          10
+thermo_modify norm yes
+
+# Set up NVE run
+
+timestep 0.5e-3
+neighbor 1.0 bin
+neigh_modify once no every 1 delay 0 check yes
+
+# Run MD
+
+velocity all create 300.0 4928459 loop geom
+fix 1 all nve
+run             ${nsteps}
+run             100
+Neighbor list info ...
+  update: every = 1 steps, delay = 0 steps, check = yes
+  max neighbors/atom: 2000, page size: 100000
+  master list distance cutoff = 6
+  ghost atom cutoff = 6
+  binsize = 3, bins = 5 5 5
+  1 neighbor lists, perpetual/occasional/extra = 1 0 0
+  (1) pair pod, perpetual
+      attributes: full, newton on
+      pair build: full/bin/atomonly
+      stencil: full/bin/3d
+      bin: standard
+Per MPI rank memory allocation (min/avg/max) = 3.187 | 3.187 | 3.187 Mbytes
+   Step          Temp          E_pair         E_mol          TotEng         Press     
+         0   300           -11.842971      0             -11.804496     -24843.054    
+        10   296.87227     -11.84257       0             -11.804496     -24609.859    
+        20   287.65971     -11.841388      0             -11.804496     -23926.722    
+        30   272.87511     -11.839492      0             -11.804496     -22841.672    
+        40   253.34724     -11.836988      0             -11.804496     -21429.268    
+        50   230.17169     -11.834015      0             -11.804496     -19782.77     
+        60   204.64408     -11.830741      0             -11.804496     -18004.755    
+        70   178.17888     -11.827347      0             -11.804495     -16197.482    
+        80   152.21769     -11.824017      0             -11.804495     -14454.425    
+        90   128.13189     -11.820928      0             -11.804495     -12854.075    
+       100   107.12666     -11.818234      0             -11.804495     -11456.437    
+Loop time of 0.153961 on 4 procs for 100 steps with 128 atoms
+
+Performance: 28.059 ns/day, 0.855 hours/ns, 649.516 timesteps/s, 83.138 katom-step/s
+96.2% CPU use with 4 MPI tasks x 1 OpenMP threads
+
+MPI task timing breakdown:
+Section |  min time  |  avg time  |  max time  |%varavg| %total
+---------------------------------------------------------------
+Pair    | 0.1281     | 0.12977    | 0.1312     |   0.3 | 84.29
+Neigh   | 0          | 0          | 0          |   0.0 |  0.00
+Comm    | 0.01967    | 0.021169   | 0.022796   |   0.8 | 13.75
+Output  | 0.00045049 | 0.00053796 | 0.00078459 |   0.0 |  0.35
+Modify  | 0.00039544 | 0.0004393  | 0.00048043 |   0.0 |  0.29
+Other   |            | 0.002049   |            |       |  1.33
+
+Nlocal:             32 ave          32 max          32 min
+Histogram: 4 0 0 0 0 0 0 0 0 0
+Nghost:            431 ave         431 max         431 min
+Histogram: 4 0 0 0 0 0 0 0 0 0
+Neighs:              0 ave           0 max           0 min
+Histogram: 4 0 0 0 0 0 0 0 0 0
+FullNghs:         1856 ave        1856 max        1856 min
+Histogram: 4 0 0 0 0 0 0 0 0 0
+
+Total # of neighbors = 7424
+Ave neighs/atom = 58
+Neighbor list builds = 0
+Dangerous builds = 0
+
+Total wall time: 0:00:00

examples/PACKAGES/pod/Ta/log.24June24.fitpod.g++.1

@@ -1,39 +1,46 @@
-LAMMPS (22 Dec 2022)
+LAMMPS (17 Apr 2024 - Development - patch_17Apr2024-179-g353121c942-modified)
+OMP_NUM_THREADS environment is not set. Defaulting to 1 thread. (src/comm.cpp:98)
   using 1 OpenMP thread(s) per MPI task
-# Demonstrate fitpod for POD potential
-
-units metal
 fitpod Ta_param.pod Ta_data.pod
-Reading potential file Ta_param.pod with DATE: 2022-11-30
 **************** Begin of POD Potentials ****************
 species: Ta 
 periodic boundary conditions: 1 1 1
+number of environment clusters: 1
+number of principal compoments: 2
 inner cut-off radius: 1
 outer cut-off radius: 5
 bessel polynomial degree: 3
 inverse polynomial degree: 6
 one-body potential: 1
-two-body potential: 3 6 6
+two-body radial basis functions: 6
-three-body potential: 3 6 5 5
+three-body radial basis functions: 5
-four-body SNAP potential: 0 0
+three-body angular degree: 4
-quadratic POD potential: 1
+four-body radial basis functions: 0
-number of basis functions for one-body potential: 1
+four-body angular degree: 0
-number of basis functions for two-body potential: 6
+five-body radial basis functions: 0
-number of basis functions for three-body potential: 25
+five-body angular degree: 0
-number of basis functions for four-body potential: 0
+six-body radial basis functions: 0
-number of descriptors for one-body potential: 1
+six-body angular degree: 0
-number of descriptors for two-body potential: 6
+seven-body radial basis functions: 0
-number of descriptors for three-body potential: 25
+seven-body angular degree: 0
-number of descriptors for four-body potential: 0
+number of local descriptors per element for one-body potential: 1
-number of descriptors for quadratic POD potential: 150
+number of local descriptors per element for two-body potential: 6
-total number of descriptors for all potentials: 182
+number of local descriptors per element for three-body potential: 25
+number of local descriptors per element for four-body potential: 0
+number of local descriptors per element for five-body potential: 0
+number of local descriptors per element for six-body potential: 0
+number of local descriptors per element for seven-body potential: 0
+number of local descriptors per element for all potentials: 32
+number of global descriptors: 32
 **************** End of POD Potentials ****************
 
 **************** Begin of Data File ****************
 file format: extxyz
 file extension: xyz
-path to training data set: ../Ta/XYZ
+path to training data set: XYZ
-path to test data set: ../Ta/XYZ
+path to test data set: XYZ
+path to environment configuration set: XYZ
+basename for output files: Ta
 training fraction: 1
 test fraction: 1
 randomize training data set: 1
@@ -45,7 +52,8 @@ energy/force calculation for test data set: 0
 fitting weight for energy: 100
 fitting weight for force: 1
 fitting weight for stress: 0
-fitting regularization parameter: 1e-10
+save pod descriptors: 0
+compute pod descriptors: 0
 **************** End of Data File ****************
 **************** Begin of Training Data Set ****************
 ---------------------------------------------------------------
@@ -74,16 +82,14 @@ maximum number of atoms: 100
 maximum number of atoms in periodic domain: 100
 maximum number of atoms in extended domain: 2700
 maximum number of neighbors in extended domain: 270000
-size of double memory: 223201
+size of double memory: 232128
-size of int memory: 14709
+size of descriptor matrix: 32 x 32
-size of descriptor matrix: 182 x 182
 **************** End of Memory Allocation ****************
 **************** Begin of Least-Squares Fitting ****************
 Configuration: # 1
 Configuration: # 101
 Configuration: # 201
 Configuration: # 301
-**************** End of Least-Squares Fitting ****************
 **************** Begin of Error Calculation ****************
 Configuration: # 1
 Configuration: # 101
@@ -94,21 +100,20 @@ Configuration: # 301
 ---------------------------------------------------------------------------------------------------
         File         | # configs |  # atoms  | MAE energy  | RMSE energy | MAE force  | RMSE force
 ---------------------------------------------------------------------------------------------------
-Displaced_A15.xyz            9         576     0.000554      0.000680      0.066393      0.083014  
+Displaced_A15.xyz            9         576     0.015324      0.015365      0.140594      0.184797  
-Displaced_BCC.xyz            9         486     0.004724      0.005103      0.108253      0.139461  
+Displaced_BCC.xyz            9         486     0.009486      0.011643      0.249983      0.320375  
-Displaced_FCC.xyz            9         432     0.001704      0.001900      0.077531      0.097471  
+Displaced_FCC.xyz            9         432     0.000686      0.000880      0.091420      0.113585  
-Elastic_BCC.xyz            100         200     0.000444      0.000446      0.000001      0.000002  
+Elastic_BCC.xyz            100         200     0.003796      0.004379      0.000015      0.000020  
-Elastic_FCC.xyz            100         400     0.000273      0.000327      0.000110      0.000163  
+Elastic_FCC.xyz            100         400     0.003332      0.003372      0.000122      0.000178  
-GSF_110.xyz                 22         528     0.001852      0.002260      0.027302      0.044765  
+GSF_110.xyz                 22         528     0.007027      0.007797      0.057637      0.115638  
-GSF_112.xyz                 22         660     0.001839      0.002404      0.051415      0.080350  
+GSF_112.xyz                 22         660     0.010396      0.011347      0.125237      0.198553  
-Liquid.xyz                   3         300     0.000674      0.000758      0.217921      0.276109  
+Liquid.xyz                   3         300     0.017584      0.023822      0.504354      0.660300  
-Surface.xyz                  7         236     0.009115      0.011661      0.047949      0.105123  
+Surface.xyz                  7         236     0.025511      0.034302      0.107190      0.285034  
-Volume_A15.xyz              30         240     0.001407      0.001693      0.000000      0.000000  
+Volume_A15.xyz              30         240     0.038624      0.048355      0.000000      0.000000  
-Volume_BCC.xyz              21          42     0.001497      0.002077      0.000000      0.000000  
+Volume_BCC.xyz              21          42     0.044423      0.061685      0.000000      0.000000  
-Volume_FCC.xyz              31         124     0.000870      0.001139      0.000000      0.000000  
+Volume_FCC.xyz              31         124     0.030062      0.041271      0.000000      0.000000  
 ---------------------------------------------------------------------------------------------------
-All files                  363        4224     0.001053      0.002171      0.059051      0.106960  
+All files                  363        4224     0.012618      0.024806      0.125879      0.247229  
 ---------------------------------------------------------------------------------------------------
 **************** End of Error Analysis for the Training Data Set ****************
-
 Total wall time: 0:00:00

examples/PACKAGES/pod/Ta/log.24June24.pod.compute.g++.1

@@ -0,0 +1,293 @@
+LAMMPS (17 Apr 2024 - Development - patch_17Apr2024-179-g353121c942-modified)
+OMP_NUM_THREADS environment is not set. Defaulting to 1 thread. (src/comm.cpp:98)
+  using 1 OpenMP thread(s) per MPI task
+# Demonstrate bispectrum computes
+
+# initialize simulation
+
+variable 	nsteps index 0
+variable 	nrep equal 2
+variable 	a equal 2.0
+units		metal
+
+# generate the box and atom positions using a BCC lattice
+
+variable 	nx equal ${nrep}
+variable 	nx equal 2
+variable 	ny equal ${nrep}
+variable 	ny equal 2
+variable 	nz equal ${nrep}
+variable 	nz equal 2
+
+boundary	p p p
+
+atom_modify	map hash
+lattice         bcc $a
+lattice         bcc 2
+Lattice spacing in x,y,z = 2 2 2
+region		box block 0 ${nx} 0 ${ny} 0 ${nz}
+region		box block 0 2 0 ${ny} 0 ${nz}
+region		box block 0 2 0 2 0 ${nz}
+region		box block 0 2 0 2 0 2
+create_box	2 box
+Created orthogonal box = (0 0 0) to (4 4 4)
+  1 by 1 by 1 MPI processor grid
+create_atoms	2 box
+Created 16 atoms
+  using lattice units in orthogonal box = (0 0 0) to (4 4 4)
+  create_atoms CPU = 0.001 seconds
+
+mass 		* 180.88
+
+displace_atoms 	all random 0.1 0.1 0.1 123456
+Displacing atoms ...
+
+# set up dummy potential to satisfy cutoff
+variable 	rcutfac equal 6.0
+pair_style 	zero ${rcutfac}
+pair_style 	zero 6
+pair_coeff 	* *
+
+# set up per-atom computes
+
+compute ld all pod/atom Ta_param.pod Ta_coefficients.pod Ta Ta
+**************** Begin of POD Potentials ****************
+species: Ta 
+periodic boundary conditions: 1 1 1
+number of environment clusters: 1
+number of principal compoments: 2
+inner cut-off radius: 1
+outer cut-off radius: 5
+bessel polynomial degree: 3
+inverse polynomial degree: 6
+one-body potential: 1
+two-body radial basis functions: 6
+three-body radial basis functions: 5
+three-body angular degree: 4
+four-body radial basis functions: 0
+four-body angular degree: 0
+five-body radial basis functions: 0
+five-body angular degree: 0
+six-body radial basis functions: 0
+six-body angular degree: 0
+seven-body radial basis functions: 0
+seven-body angular degree: 0
+number of local descriptors per element for one-body potential: 1
+number of local descriptors per element for two-body potential: 6
+number of local descriptors per element for three-body potential: 25
+number of local descriptors per element for four-body potential: 0
+number of local descriptors per element for five-body potential: 0
+number of local descriptors per element for six-body potential: 0
+number of local descriptors per element for seven-body potential: 0
+number of local descriptors per element for all potentials: 32
+number of global descriptors: 32
+**************** End of POD Potentials ****************
+
+**************** Begin of Model Coefficients ****************
+total number of coefficients for POD potential: 32
+total number of elements for PCA projection matrix: 0
+total number of elements for PCA centroids: 0
+**************** End of Model Coefficients ****************
+
+compute dd all podd/atom Ta_param.pod Ta_coefficients.pod Ta Ta
+**************** Begin of POD Potentials ****************
+species: Ta 
+periodic boundary conditions: 1 1 1
+number of environment clusters: 1
+number of principal compoments: 2
+inner cut-off radius: 1
+outer cut-off radius: 5
+bessel polynomial degree: 3
+inverse polynomial degree: 6
+one-body potential: 1
+two-body radial basis functions: 6
+three-body radial basis functions: 5
+three-body angular degree: 4
+four-body radial basis functions: 0
+four-body angular degree: 0
+five-body radial basis functions: 0
+five-body angular degree: 0
+six-body radial basis functions: 0
+six-body angular degree: 0
+seven-body radial basis functions: 0
+seven-body angular degree: 0
+number of local descriptors per element for one-body potential: 1
+number of local descriptors per element for two-body potential: 6
+number of local descriptors per element for three-body potential: 25
+number of local descriptors per element for four-body potential: 0
+number of local descriptors per element for five-body potential: 0
+number of local descriptors per element for six-body potential: 0
+number of local descriptors per element for seven-body potential: 0
+number of local descriptors per element for all potentials: 32
+number of global descriptors: 32
+**************** End of POD Potentials ****************
+
+**************** Begin of Model Coefficients ****************
+total number of coefficients for POD potential: 32
+total number of elements for PCA projection matrix: 0
+total number of elements for PCA centroids: 0
+**************** End of Model Coefficients ****************
+
+
+# set up compute snap generating global array
+
+compute gdd all pod/global Ta_param.pod Ta_coefficients.pod Ta Ta
+**************** Begin of POD Potentials ****************
+species: Ta 
+periodic boundary conditions: 1 1 1
+number of environment clusters: 1
+number of principal compoments: 2
+inner cut-off radius: 1
+outer cut-off radius: 5
+bessel polynomial degree: 3
+inverse polynomial degree: 6
+one-body potential: 1
+two-body radial basis functions: 6
+three-body radial basis functions: 5
+three-body angular degree: 4
+four-body radial basis functions: 0
+four-body angular degree: 0
+five-body radial basis functions: 0
+five-body angular degree: 0
+six-body radial basis functions: 0
+six-body angular degree: 0
+seven-body radial basis functions: 0
+seven-body angular degree: 0
+number of local descriptors per element for one-body potential: 1
+number of local descriptors per element for two-body potential: 6
+number of local descriptors per element for three-body potential: 25
+number of local descriptors per element for four-body potential: 0
+number of local descriptors per element for five-body potential: 0
+number of local descriptors per element for six-body potential: 0
+number of local descriptors per element for seven-body potential: 0
+number of local descriptors per element for all potentials: 32
+number of global descriptors: 32
+**************** End of POD Potentials ****************
+
+**************** Begin of Model Coefficients ****************
+total number of coefficients for POD potential: 32
+total number of elements for PCA projection matrix: 0
+total number of elements for PCA centroids: 0
+**************** End of Model Coefficients ****************
+
+#fix 		gdd all ave/time 1 1 1 c_gdd[*] file pod.gdd.dat mode vector
+
+compute ldd all pod/local Ta_param.pod Ta_coefficients.pod Ta Ta
+**************** Begin of POD Potentials ****************
+species: Ta 
+periodic boundary conditions: 1 1 1
+number of environment clusters: 1
+number of principal compoments: 2
+inner cut-off radius: 1
+outer cut-off radius: 5
+bessel polynomial degree: 3
+inverse polynomial degree: 6
+one-body potential: 1
+two-body radial basis functions: 6
+three-body radial basis functions: 5
+three-body angular degree: 4
+four-body radial basis functions: 0
+four-body angular degree: 0
+five-body radial basis functions: 0
+five-body angular degree: 0
+six-body radial basis functions: 0
+six-body angular degree: 0
+seven-body radial basis functions: 0
+seven-body angular degree: 0
+number of local descriptors per element for one-body potential: 1
+number of local descriptors per element for two-body potential: 6
+number of local descriptors per element for three-body potential: 25
+number of local descriptors per element for four-body potential: 0
+number of local descriptors per element for five-body potential: 0
+number of local descriptors per element for six-body potential: 0
+number of local descriptors per element for seven-body potential: 0
+number of local descriptors per element for all potentials: 32
+number of global descriptors: 32
+**************** End of POD Potentials ****************
+
+**************** Begin of Model Coefficients ****************
+total number of coefficients for POD potential: 32
+total number of elements for PCA projection matrix: 0
+total number of elements for PCA centroids: 0
+**************** End of Model Coefficients ****************
+
+#fix 		ldd all ave/time 1 1 1 c_ldd[*] file pod.ldd.dat mode vector
+
+#dump 		mydump_ld all custom 1000 dump_ld id c_ld[*]
+#dump 		mydump_dd all custom 1000 dump_dd id c_dd[*]
+
+variable sample_ld1 equal C_ld[1][10]  # Arbitrary local descriptor
+fix ldprint all print 1 "${sample_ld1}"
+
+run             ${nsteps}
+run             0
+WARNING: No fixes with time integration, atoms won't move (src/verlet.cpp:60)
+Generated 0 of 1 mixed pair_coeff terms from geometric mixing rule
+WARNING: More than one compute pod (src/ML-POD/compute_pod_atom.cpp:87)
+WARNING: More than one compute pod (src/ML-POD/compute_podd_atom.cpp:87)
+WARNING: More than one compute pod (src/ML-POD/compute_pod_global.cpp:87)
+WARNING: More than one compute pod (src/ML-POD/compute_pod_local.cpp:89)
+Neighbor list info ...
+  update: every = 1 steps, delay = 0 steps, check = yes
+  max neighbors/atom: 2000, page size: 100000
+  master list distance cutoff = 8
+  ghost atom cutoff = 8
+  binsize = 4, bins = 1 1 1
+  5 neighbor lists, perpetual/occasional/extra = 1 4 0
+  (1) pair zero, perpetual
+      attributes: half, newton on
+      pair build: half/bin/atomonly/newton
+      stencil: half/bin/3d
+      bin: standard
+  (2) compute pod/atom, occasional
+      attributes: full, newton on
+      pair build: full/bin/atomonly
+      stencil: full/bin/3d
+      bin: standard
+  (3) compute podd/atom, occasional
+      attributes: full, newton on
+      pair build: full/bin/atomonly
+      stencil: full/bin/3d
+      bin: standard
+  (4) compute pod/global, occasional
+      attributes: full, newton on
+      pair build: full/bin/atomonly
+      stencil: full/bin/3d
+      bin: standard
+  (5) compute pod/local, occasional
+      attributes: full, newton on
+      pair build: full/bin/atomonly
+      stencil: full/bin/3d
+      bin: standard
+0.344594831165384
+Per MPI rank memory allocation (min/avg/max) = 6.326 | 6.326 | 6.326 Mbytes
+   Step          Temp          E_pair         E_mol          TotEng         Press     
+         0   0              0              0              0              0            
+Loop time of 1.23e-06 on 1 procs for 0 steps with 16 atoms
+
+243.9% CPU use with 1 MPI tasks x 1 OpenMP threads
+
+MPI task timing breakdown:
+Section |  min time  |  avg time  |  max time  |%varavg| %total
+---------------------------------------------------------------
+Pair    | 0          | 0          | 0          |   0.0 |  0.00
+Neigh   | 0          | 0          | 0          |   0.0 |  0.00
+Comm    | 0          | 0          | 0          |   0.0 |  0.00
+Output  | 0          | 0          | 0          |   0.0 |  0.00
+Modify  | 0          | 0          | 0          |   0.0 |  0.00
+Other   |            | 1.23e-06   |            |       |100.00
+
+Nlocal:             16 ave          16 max          16 min
+Histogram: 1 0 0 0 0 0 0 0 0 0
+Nghost:           1984 ave        1984 max        1984 min
+Histogram: 1 0 0 0 0 0 0 0 0 0
+Neighs:           4311 ave        4311 max        4311 min
+Histogram: 1 0 0 0 0 0 0 0 0 0
+FullNghs:         8623 ave        8623 max        8623 min
+Histogram: 1 0 0 0 0 0 0 0 0 0
+
+Total # of neighbors = 8623
+Ave neighs/atom = 538.9375
+Neighbor list builds = 0
+Dangerous builds = 0
+Total wall time: 0:00:00

examples/PACKAGES/pod/Ta/log.4Jan23.pod.g++.1

@@ -1,142 +0,0 @@
-LAMMPS (22 Dec 2022)
-  using 1 OpenMP thread(s) per MPI task
-# Demonstrate POD Ta potential
-
-# Initialize simulation
-
-variable nsteps index 100
-variable nrep equal 4
-variable a equal 3.316
-units           metal
-
-# generate the box and atom positions using a BCC lattice
-
-variable nx equal ${nrep}
-variable nx equal 4
-variable ny equal ${nrep}
-variable ny equal 4
-variable nz equal ${nrep}
-variable nz equal 4
-
-boundary        p p p
-
-lattice         bcc $a
-lattice         bcc 3.316
-Lattice spacing in x,y,z = 3.316 3.316 3.316
-region          box block 0 ${nx} 0 ${ny} 0 ${nz}
-region          box block 0 4 0 ${ny} 0 ${nz}
-region          box block 0 4 0 4 0 ${nz}
-region          box block 0 4 0 4 0 4
-create_box      1 box
-Created orthogonal box = (0 0 0) to (13.264 13.264 13.264)
-  1 by 1 by 1 MPI processor grid
-create_atoms    1 box
-Created 128 atoms
-  using lattice units in orthogonal box = (0 0 0) to (13.264 13.264 13.264)
-  create_atoms CPU = 0.000 seconds
-
-mass 1 180.88
-
-
-# POD potential
-pair_style pod
-pair_coeff * * Ta_param.pod Ta_coeff.pod Ta
-Reading potential file Ta_param.pod with DATE: 2022-11-30
-**************** Begin of POD Potentials ****************
-species: Ta 
-periodic boundary conditions: 1 1 1
-inner cut-off radius: 1
-outer cut-off radius: 5
-bessel polynomial degree: 3
-inverse polynomial degree: 6
-one-body potential: 1
-two-body potential: 3 6 6
-three-body potential: 3 6 5 5
-four-body SNAP potential: 0 0
-quadratic POD potential: 0
-number of basis functions for one-body potential: 1
-number of basis functions for two-body potential: 6
-number of basis functions for three-body potential: 25
-number of basis functions for four-body potential: 0
-number of descriptors for one-body potential: 1
-number of descriptors for two-body potential: 6
-number of descriptors for three-body potential: 25
-number of descriptors for four-body potential: 0
-number of descriptors for quadratic POD potential: 0
-total number of descriptors for all potentials: 32
-**************** End of POD Potentials ****************
-
-
-# Setup output
-
-thermo          10
-thermo_modify norm yes
-
-# Set up NVE run
-
-timestep 0.5e-3
-neighbor 1.0 bin
-neigh_modify once no every 1 delay 0 check yes
-
-# Run MD
-
-velocity all create 300.0 4928459 loop geom
-fix 1 all nve
-run             ${nsteps}
-run             100
-Neighbor list info ...
-  update: every = 1 steps, delay = 0 steps, check = yes
-  max neighbors/atom: 2000, page size: 100000
-  master list distance cutoff = 6
-  ghost atom cutoff = 6
-  binsize = 3, bins = 5 5 5
-  1 neighbor lists, perpetual/occasional/extra = 1 0 0
-  (1) pair pod, perpetual
-      attributes: full, newton on
-      pair build: full/bin/atomonly
-      stencil: full/bin/3d
-      bin: standard
-Per MPI rank memory allocation (min/avg/max) = 3.082 | 3.082 | 3.082 Mbytes
-   Step          Temp          E_pair         E_mol          TotEng         Press     
-         0   300           -11.841512      0             -11.803037     -15933.622    
-        10   296.91721     -11.841117      0             -11.803037     -15691.904    
-        20   287.83555     -11.839952      0             -11.803037     -14982.977    
-        30   273.25574     -11.838082      0             -11.803037     -13853.44     
-        40   253.98821     -11.835611      0             -11.803037     -12375.459    
-        50   231.10664     -11.832676      0             -11.803037     -10639.774    
-        60   205.8844      -11.829441      0             -11.803037     -8747.2222    
-        70   179.71599     -11.826085      0             -11.803037     -6799.8371    
-        80   154.02711     -11.822791      0             -11.803037     -4892.7805    
-        90   130.17821     -11.819732      0             -11.803036     -3108.1226    
-       100   109.36842     -11.817063      0             -11.803036     -1510.9592    
-Loop time of 1.51641 on 1 procs for 100 steps with 128 atoms
-
-Performance: 2.849 ns/day, 8.425 hours/ns, 65.945 timesteps/s, 8.441 katom-step/s
-99.9% CPU use with 1 MPI tasks x 1 OpenMP threads
-
-MPI task timing breakdown:
-Section |  min time  |  avg time  |  max time  |%varavg| %total
----------------------------------------------------------------
-Pair    | 1.5158     | 1.5158     | 1.5158     |   0.0 | 99.96
-Neigh   | 0          | 0          | 0          |   0.0 |  0.00
-Comm    | 0.00023616 | 0.00023616 | 0.00023616 |   0.0 |  0.02
-Output  | 0.00010779 | 0.00010779 | 0.00010779 |   0.0 |  0.01
-Modify  | 9.7284e-05 | 9.7284e-05 | 9.7284e-05 |   0.0 |  0.01
-Other   |            | 0.0001254  |            |       |  0.01
-
-Nlocal:            128 ave         128 max         128 min
-Histogram: 1 0 0 0 0 0 0 0 0 0
-Nghost:            727 ave         727 max         727 min
-Histogram: 1 0 0 0 0 0 0 0 0 0
-Neighs:              0 ave           0 max           0 min
-Histogram: 1 0 0 0 0 0 0 0 0 0
-FullNghs:         7424 ave        7424 max        7424 min
-Histogram: 1 0 0 0 0 0 0 0 0 0
-
-Total # of neighbors = 7424
-Ave neighs/atom = 58
-Neighbor list builds = 0
-Dangerous builds = 0
-
-
-Total wall time: 0:00:01

examples/PACKAGES/pod/Ta/log.4Jan23.pod.g++.4

@@ -1,142 +0,0 @@
-LAMMPS (22 Dec 2022)
-  using 1 OpenMP thread(s) per MPI task
-# Demonstrate POD Ta potential
-
-# Initialize simulation
-
-variable nsteps index 100
-variable nrep equal 4
-variable a equal 3.316
-units           metal
-
-# generate the box and atom positions using a BCC lattice
-
-variable nx equal ${nrep}
-variable nx equal 4
-variable ny equal ${nrep}
-variable ny equal 4
-variable nz equal ${nrep}
-variable nz equal 4
-
-boundary        p p p
-
-lattice         bcc $a
-lattice         bcc 3.316
-Lattice spacing in x,y,z = 3.316 3.316 3.316
-region          box block 0 ${nx} 0 ${ny} 0 ${nz}
-region          box block 0 4 0 ${ny} 0 ${nz}
-region          box block 0 4 0 4 0 ${nz}
-region          box block 0 4 0 4 0 4
-create_box      1 box
-Created orthogonal box = (0 0 0) to (13.264 13.264 13.264)
-  1 by 2 by 2 MPI processor grid
-create_atoms    1 box
-Created 128 atoms
-  using lattice units in orthogonal box = (0 0 0) to (13.264 13.264 13.264)
-  create_atoms CPU = 0.000 seconds
-
-mass 1 180.88
-
-
-# POD potential
-pair_style pod
-pair_coeff * * Ta_param.pod Ta_coeff.pod Ta
-Reading potential file Ta_param.pod with DATE: 2022-11-30
-**************** Begin of POD Potentials ****************
-species: Ta 
-periodic boundary conditions: 1 1 1
-inner cut-off radius: 1
-outer cut-off radius: 5
-bessel polynomial degree: 3
-inverse polynomial degree: 6
-one-body potential: 1
-two-body potential: 3 6 6
-three-body potential: 3 6 5 5
-four-body SNAP potential: 0 0
-quadratic POD potential: 0
-number of basis functions for one-body potential: 1
-number of basis functions for two-body potential: 6
-number of basis functions for three-body potential: 25
-number of basis functions for four-body potential: 0
-number of descriptors for one-body potential: 1
-number of descriptors for two-body potential: 6
-number of descriptors for three-body potential: 25
-number of descriptors for four-body potential: 0
-number of descriptors for quadratic POD potential: 0
-total number of descriptors for all potentials: 32
-**************** End of POD Potentials ****************
-
-
-# Setup output
-
-thermo          10
-thermo_modify norm yes
-
-# Set up NVE run
-
-timestep 0.5e-3
-neighbor 1.0 bin
-neigh_modify once no every 1 delay 0 check yes
-
-# Run MD
-
-velocity all create 300.0 4928459 loop geom
-fix 1 all nve
-run             ${nsteps}
-run             100
-Neighbor list info ...
-  update: every = 1 steps, delay = 0 steps, check = yes
-  max neighbors/atom: 2000, page size: 100000
-  master list distance cutoff = 6
-  ghost atom cutoff = 6
-  binsize = 3, bins = 5 5 5
-  1 neighbor lists, perpetual/occasional/extra = 1 0 0
-  (1) pair pod, perpetual
-      attributes: full, newton on
-      pair build: full/bin/atomonly
-      stencil: full/bin/3d
-      bin: standard
-Per MPI rank memory allocation (min/avg/max) = 3.062 | 3.062 | 3.062 Mbytes
-   Step          Temp          E_pair         E_mol          TotEng         Press     
-         0   300           -11.841512      0             -11.803037     -15933.622    
-        10   296.91721     -11.841117      0             -11.803037     -15691.904    
-        20   287.83555     -11.839952      0             -11.803037     -14982.977    
-        30   273.25574     -11.838082      0             -11.803037     -13853.44     
-        40   253.98821     -11.835611      0             -11.803037     -12375.459    
-        50   231.10664     -11.832676      0             -11.803037     -10639.774    
-        60   205.8844      -11.829441      0             -11.803037     -8747.2222    
-        70   179.71599     -11.826085      0             -11.803037     -6799.8371    
-        80   154.02711     -11.822791      0             -11.803037     -4892.7805    
-        90   130.17821     -11.819732      0             -11.803036     -3108.1226    
-       100   109.36842     -11.817063      0             -11.803036     -1510.9592    
-Loop time of 0.437423 on 4 procs for 100 steps with 128 atoms
-
-Performance: 9.876 ns/day, 2.430 hours/ns, 228.612 timesteps/s, 29.262 katom-step/s
-98.0% CPU use with 4 MPI tasks x 1 OpenMP threads
-
-MPI task timing breakdown:
-Section |  min time  |  avg time  |  max time  |%varavg| %total
----------------------------------------------------------------
-Pair    | 0.41133    | 0.41882    | 0.42464    |   0.7 | 95.75
-Neigh   | 0          | 0          | 0          |   0.0 |  0.00
-Comm    | 0.011279   | 0.017302   | 0.024975   |   3.7 |  3.96
-Output  | 0.00012956 | 0.00029493 | 0.00077991 |   0.0 |  0.07
-Modify  | 4.2093e-05 | 4.7838e-05 | 5.3039e-05 |   0.0 |  0.01
-Other   |            | 0.0009598  |            |       |  0.22
-
-Nlocal:             32 ave          32 max          32 min
-Histogram: 4 0 0 0 0 0 0 0 0 0
-Nghost:            431 ave         431 max         431 min
-Histogram: 4 0 0 0 0 0 0 0 0 0
-Neighs:              0 ave           0 max           0 min
-Histogram: 4 0 0 0 0 0 0 0 0 0
-FullNghs:         1856 ave        1856 max        1856 min
-Histogram: 4 0 0 0 0 0 0 0 0 0
-
-Total # of neighbors = 7424
-Ave neighs/atom = 58
-Neighbor list builds = 0
-Dangerous builds = 0
-
-
-Total wall time: 0:00:00

examples/PACKAGES/pod/Ta_Quadratic/Ta_coefficients.pod

@@ -1,183 +0,0 @@
-POD_coefficients: 182
--4.35182  
-3.57837   
-2.25497   
-4.84612   
--2.06319  
--1.17070  
--0.23842  
-9.17160   
-36.02366  
-16.65304  
--141.18403
-37.17722  
-0.46028   
--9.76148  
--0.03681  
-15.64520  
-2.29791   
-0.02143   
-2.69735   
--0.35336  
-0.51108   
--2.36290  
-0.18617   
--0.13079  
-1.02666   
-0.21514   
-0.08075   
--0.28347  
--0.45059  
--0.24762  
--1.13671  
--0.30577  
-0.60504   
-0.31285   
--0.10639  
--0.06957  
-0.21961   
--0.10426  
-0.80318   
--11.41460 
--10.26102 
--0.03887  
--18.86071 
--4.47372  
--1.76858  
--0.92503  
-0.42654   
-0.35849   
-0.56611   
--0.79354  
-5.65136   
-8.75283   
--6.22283  
--4.34623  
-10.20031  
-6.53360   
-7.16688   
-2.19236   
-5.90789   
-3.52173   
-7.97264   
-0.21104   
--0.01015  
-0.01023   
-0.03088   
-0.10222   
-0.05366   
--0.08037  
--3.17612  
--3.45669  
--0.79282  
--2.38323  
--0.69797  
--1.44780  
--0.03351  
--0.05645  
-0.01901   
--0.01923  
-0.05401   
--0.02095  
-1.45651   
-1.58812   
-1.41188   
-2.18122   
-3.04893   
-1.09294   
-3.03781   
-1.07249   
-0.50262   
-0.81150   
-0.35997   
-0.64602   
--0.04245  
-0.00113   
--0.02894  
-0.04382   
--0.06556  
-0.00052   
-4.67541   
-0.11812   
-1.52428   
--0.17075  
-0.20231   
-0.36857   
-0.61744   
-0.20190   
--0.00816  
-0.16194   
--0.12948  
--0.02136  
--2.19271  
-0.62510   
-0.20030   
--0.27621  
--0.58116  
--0.21792  
--1.82295  
--0.32166  
--0.64550  
--0.11580  
--0.02438  
--0.08057  
-0.19538   
-0.04119   
-0.00323   
-0.06530   
--0.02547  
--0.01404  
-0.22336   
--0.48191  
--0.10715  
--0.25685  
--0.65069  
--0.31428  
--0.06947  
-0.11924   
-0.05467   
-0.12105   
--0.03980  
--0.00295  
--2.14413  
-0.82345   
-0.23083   
--0.24925  
--0.36678  
--0.16709  
-1.20410   
--0.47756  
--0.11104  
-0.09587   
-0.03722   
-0.00309   
--0.29879  
--0.06463  
--0.10236  
--0.02276  
--0.06012  
--0.02985  
-12.06876  
--3.39995  
-0.85590   
--0.77481  
--1.13392  
--0.40511  
--0.08005  
--0.07162  
--0.05978  
--0.02407  
--0.06031  
--0.02307  
--10.24105 
-2.49356   
--1.14052  
-0.70453   
-0.99988   
-0.33862   
-2.43469   
--1.16557  
--0.23708  
-0.03482   
--0.05280  
--0.02735  

examples/PACKAGES/pod/Ta_Quadratic/Ta_param.pod

@@ -1,33 +0,0 @@
-# DATE: 2022-11-30 UNITS: metal CONTRIBUTOR: Ngoc Cuong Nguyen, exapde@gmail.com CITATION:  https://arxiv.org/abs/2209.02362
-# chemical element symbols
-species Ta
-
-# periodic boundary conditions
-pbc 1 1 1
-
-# inner cut-off radius
-rin 1.0
-
-# outer cut-off radius
-rcut 5.0
-
-# polynomial degrees for radial basis functions
-bessel_polynomial_degree 3
-inverse_polynomial_degree 6
-
-# one-body potential
-onebody 1
-
-# two-body linear POD potential
-twobody_number_radial_basis_functions 6
-
-# three-body linear POD potential
-threebody_number_radial_basis_functions 5
-threebody_number_angular_basis_functions 5
-
-# four-body linear SNAP potential
-fourbody_snap_twojmax 0 
-
-# quadratic POD potential
-quadratic_pod_potential 1
-

examples/PACKAGES/pod/Ta_Quadratic/Ta_training_analysis.pod

@@ -1,387 +0,0 @@
-# Displaced_A15.xyz
-  config   # atoms      energy        DFT energy     energy error     force          DFT force       force error
-     1         64    -754.2481469    -754.220443     0.0004328739544 8.011514562     8.398670477     0.06376624845   
-     2         64    -753.8045629    -753.865255     0.0009483144042 9.036674821     9.134430545     0.07283326238   
-     3         64    -754.1013214    -754.0221       0.001237834258  8.637024088     9.017261102     0.06364800593   
-     4         64    -754.2847414    -754.279613     8.013173542e-05 8.107730622     8.381725092     0.06510174353   
-     5         64    -753.8382044    -753.777209     0.0009530527364 9.104258904     9.478314477     0.07200164536   
-     6         64    -754.0793448    -754.048643     0.0004797149286 8.152198894     8.465317938     0.06707941365   
-     7         64    -754.3310528    -754.317603     0.0002101531052 7.9440922       8.127690491     0.05987172107   
-     8         64    -754.0070856    -753.969161     0.0005925720361 9.179443805     9.425464952     0.06695320222   
-     9         64    -754.1450602    -754.141988     4.800358611e-05 8.574170786     8.821346913     0.06628506232   
-# Displaced_BCC.xyz
-  config   # atoms      energy        DFT energy     energy error     force          DFT force       force error
-    10         54    -630.8081935    -631.019667     0.003916175555  15.97497534     16.625876       0.1021118679    
-    11         54    -631.4580134    -631.719595     0.004844103559  15.24068949     15.58666626     0.1043856792    
-    12         54    -631.1667566    -631.386255     0.004064785931  15.46091788     15.92378883     0.1062824093    
-    13         54    -632.3004944    -632.575826     0.005098733346  14.4261974      14.55977162     0.0983914465    
-    14         54    -630.089475     -630.450212     0.006680315456  16.78432947     16.96340726     0.1085102316    
-    15         54    -631.3402507    -631.669379     0.006094968558  15.8289421      16.05757315     0.1000888617    
-    16         54    -632.0447348    -632.431277     0.007158189539  14.73098416     14.69810718     0.09621569386   
-    17         54    -630.7186536    -630.960068     0.004470636457  15.62236511     15.99073148     0.1063789621    
-    18         54    -623.3884977    -623.378198     0.0001907343232 23.9739298      24.67640432     0.1519105596    
-# Displaced_FCC.xyz
-  config   # atoms      energy        DFT energy     energy error     force          DFT force       force error
-    19         48    -556.0112403    -555.899463     0.002328692864  5.300795546     6.084617063     0.07215982294   
-    20         48    -555.9884377    -555.922478     0.001374159425  5.509767245     6.297071211     0.08438730171   
-    21         48    -555.8765558    -555.800269     0.001589309295  5.420812146     6.021098636     0.07404418561   
-    22         48    -556.2511475    -556.196151     0.001145760427  4.541854917     5.127955094     0.06609455537   
-    23         48    -555.6590668    -555.488929     0.003544536845  6.087063152     7.050223459     0.09107542897   
-    24         48    -556.1020655    -556.027926     0.001544573067  5.048523277     5.611881174     0.06751584111   
-    25         48    -556.0607474    -555.968399     0.001923924855  5.209756732     5.979217189     0.08024047849   
-    26         48    -556.0598015    -556.047132     0.0002639485133 4.995519804     5.544452585     0.07745361595   
-    27         48    -555.8256424    -555.747848     0.00162071731   5.762702675     6.47892568      0.08480576837   
-# Elastic_BCC.xyz
-  config   # atoms      energy        DFT energy     energy error     force          DFT force       force error
-    28          2    -23.69025375    -23.689367      0.0004433751768 0.0006229111456 0.0006222748589 9.850534294e-07 
-    29          2    -23.690768      -23.689888      0.0004399996606 0.0006181832344 0.0006166052222 1.005063831e-06 
-    30          2    -23.69082186    -23.689996      0.0004129292199 0.0008798076914 0.0008810425642 1.748431771e-06 
-    31          2    -23.69166748    -23.690957      0.0003552395228 1.000599546e-06 0               4.011214433e-07 
-    32          2    -23.69137648    -23.690521      0.0004277406839 0.0005992884516 0.0005982273815 7.219402767e-07 
-    33          2    -23.69120607    -23.69038       0.000413036746  0.000594795449  0.0005925723585 9.949794864e-07 
-    34          2    -23.6900782     -23.689202      0.000438099978  0.0006263336007 0.0006279363025 1.111474332e-06 
-    35          2    -23.69121642    -23.690482      0.0003672088475 0.00086350893   0.0008640138888 1.400551425e-06 
-    36          2    -23.69074792    -23.689902      0.0004229601404 0.0006176589245 0.0006152154094 9.894995842e-07 
-    37          2    -23.6914111     -23.690563      0.0004240514006 0.0006052368582 0.0006038725031 4.148713688e-07 
-    38          2    -23.69095105    -23.690207      0.0003720253444 0.001071999394  0.00107369735   7.195087511e-07 
-    39          2    -23.69007856    -23.689285      0.0003967806815 0.0008875291033 0.000890013483  1.187797446e-06 
-    40          2    -23.69061639    -23.689768      0.0004241940528 0.00107874486   0.001080249045  1.09850755e-06  
-    41          2    -23.69064479    -23.68968       0.0004823957182 0.0008702114429 0.0008680034562 8.482668094e-07 
-    42          2    -23.6910243     -23.690074      0.0004751495365 0.001368926593  0.001373818765  2.351835771e-06 
-    43          2    -23.68910107    -23.688108      0.0004965341502 0.0006334704764 0.0006336134468 5.990110163e-07 
-    44          2    -23.69003986    -23.689241      0.0003994287496 0.0008886654529 0.0008880101351 1.319380731e-06 
-    45          2    -23.69042994    -23.68952       0.0004549677771 0.0008868888968 0.0008860011287 4.688590432e-07 
-    46          2    -23.68738487    -23.686278      0.0005534329248 0.0006426681164 0.0006406777661 9.718938063e-07 
-    47          2    -23.69095089    -23.690097      0.0004269463837 0.0008409065407 0.0008410160522 1.331153983e-06 
-    48          2    -23.69158161    -23.690811      0.0003853032969 0.0008464480591 0.0008500070588 1.611890257e-06 
-    49          2    -23.69114597    -23.690266      0.0004399838162 0.001039354626  0.001044322747  3.354760892e-06 
-    50          2    -23.6914223     -23.690597      0.0004126524984 0.001045529019  0.001050833003  2.164890519e-06 
-    51          2    -23.69157045    -23.690673      0.000448723371  0.0006045419676 0.0006038907186 7.138092253e-07 
-    52          2    -23.69135377    -23.690551      0.0004013838132 0.0008554941993 0.0008590064028 1.199818147e-06 
-    53          2    -23.6914855     -23.690693      0.0003962481391 0.0008561040807 0.0008590110593 1.062310127e-06 
-    54          2    -23.69110782    -23.69021       0.0004489100066 0.0008699576152 0.0008730051546 1.100920756e-06 
-    55          2    -23.68987142    -23.688943      0.0004642105928 0.0008789741194 0.0008800306813 8.92018913e-07  
-    56          2    -23.69108099    -23.690136      0.0004724937378 0.0005971006713 0.000593996633  9.809423198e-07 
-    57          2    -23.6884849     -23.687444      0.0005204491042 0.000904649919  0.000903059245  1.159812589e-06 
-    58          2    -23.69061659    -23.689801      0.0004077963743 0.0008734822906 0.0008740011442 2.825876968e-07 
-    59          2    -23.69129673    -23.690408      0.0004443659273 8.294238722e-07 0               3.094976672e-07 
-    60          2    -23.69128183    -23.690362      0.0004599146039 0.0006083806397 0.0006067503605 7.610598464e-07 
-    61          2    -23.68992958    -23.688881      0.0005242884644 0.000821029922  0.0008250054545 1.71686782e-06  
-    62          2    -23.6913441     -23.690515      0.0004145518648 0.001475621399  0.001475779794  2.84677577e-06  
-    63          2    -23.69141171    -23.690551      0.0004303564504 0.0005957866015 0.0005996599036 1.20514709e-06  
-    64          2    -23.69029628    -23.689487      0.0004046403158 0.0006212225944 0.0006194384554 9.873937532e-07 
-    65          2    -23.69072139    -23.68986       0.0004306945962 0.0008858828979 0.0008860124153 5.860284088e-07 
-    66          2    -23.69018379    -23.689288      0.0004478949008 0.001400963016  0.001396479144  1.244329984e-06 
-    67          2    -23.69129611    -23.690457      0.0004195546182 0.0005914019669 0.0005939831647 1.147186262e-06 
-    68          2    -23.69084551    -23.689792      0.0005267528672 0.0008274902414 0.0008340587509 2.923475453e-06 
-    69          2    -23.69101454    -23.690006      0.0005042723904 0.0005874526839 0.0005897694465 1.183912924e-06 
-    70          2    -23.69137638    -23.690571      0.000402691994  0.0005935054979 0.0005939781141 8.884918862e-07 
-    71          2    -23.69114123    -23.690213      0.0004641143201 0.001085937193  0.001084315452  6.623820068e-07 
-    72          2    -23.69146017    -23.690617      0.0004215869658 0.0005980165481 0.0006024682564 1.268404944e-06 
-    73          2    -23.69063494    -23.689761      0.0004369696294 0.0008787872001 0.0008790688255 2.274049375e-06 
-    74          2    -23.69116059    -23.69027       0.0004452958397 6.913233052e-07 0               2.060281613e-07 
-    75          2    -23.69134793    -23.690599      0.0003744660576 0.0006108390866 0.0006137752031 6.96527736e-07  
-    76          2    -23.69149586    -23.69061       0.0004429283645 9.198413091e-07 0               3.754401369e-07 
-    77          2    -23.69139951    -23.690603      0.0003982565418 0.0008543320292 0.0008590331775 1.578633627e-06 
-    78          2    -23.68884519    -23.687908      0.0004685934904 0.0009053957054 0.0009010105438 1.657834627e-06 
-    79          2    -23.69142551    -23.690688      0.0003687527847 0.0008461959647 0.0008470064935 1.246502358e-06 
-    80          2    -23.69088798    -23.689988      0.0004499883039 0.0006191457459 0.0006194465272 7.974697206e-07 
-    81          2    -23.69054504    -23.689613      0.0004660181693 0.0008740608763 0.0008740732235 7.595219281e-07 
-    82          2    -23.69150291    -23.690678      0.0004124547512 0.000610815565  0.0006123757017 8.071847352e-07 
-    83          2    -23.69107508    -23.69017       0.0004525405781 0.0008712164372 0.0008750051428 1.391960695e-06 
-    84          2    -23.68888774    -23.687892      0.0004978720826 0.001115255323  0.001112070142  1.300271383e-06 
-    85          2    -23.69100617    -23.690132      0.0004370853773 0.0008623539978 0.000868018433  1.989797184e-06 
-    86          2    -23.69156961    -23.690843      0.0003633026522 0.0006034844173 0.0006081134763 1.367563513e-06 
-    87          2    -23.6914135     -23.690598      0.0004077495027 0.001205622469  0.001217674833  4.139579599e-06 
-    88          2    -23.69152569    -23.690656      0.0004348453461 0.0005982210923 0.0006024765556 1.339909066e-06 
-    89          2    -23.69122964    -23.690254      0.00048782182   0.001039614512  0.001043496047  2.818899799e-06 
-    90          2    -23.69160573    -23.690694      0.0004558641588 0.0006005238032 0.0006010740387 4.468144277e-07 
-    91          2    -23.69097667    -23.690097      0.0004398327929 0.0008742196236 0.0008730234819 9.401054078e-07 
-    92          2    -23.68931978    -23.688402      0.000458891277  0.0006323492378 0.000632180354  2.788895255e-07 
-    93          2    -23.68957636    -23.688669      0.0004536814608 0.001093068336  0.001092474256  1.597403354e-06 
-    94          2    -23.69136079    -23.690538      0.0004113951269 0.0008559692215 0.0008610145179 1.717480332e-06 
-    95          2    -23.69064046    -23.689722      0.0004592296819 0.0006203235661 0.0006251287867 1.466428815e-06 
-    96          2    -23.69148677    -23.690581      0.0004528827615 7.127210559e-07 0               2.255863159e-07 
-    97          2    -23.68967251    -23.688755      0.0004587561741 0.0006269092047 0.0006251143895 8.456044924e-07 
-    98          2    -23.69038245    -23.689312      0.0005352258985 0.0008260738577 0.0008290597083 1.434578094e-06 
-    99          2    -23.6885155     -23.687388      0.000563750435  0.001127068066  0.001120237475  2.790106364e-06 
-   100          2    -23.69147138    -23.690664      0.0004036883861 0.0006101343713 0.0006109402589 2.333308226e-07 
-   101          2    -23.69059185    -23.68941       0.0005909264985 0.0005851627979 0.0005883553348 1.578359791e-06 
-   102          2    -23.69082355    -23.690035      0.0003942730081 0.0008795919888 0.0008810062429 8.322915827e-07 
-   103          2    -23.69101815    -23.690015      0.0005015766298 0.0008420116739 0.0008450195264 1.339928081e-06 
-   104          2    -23.6915919     -23.690752      0.0004199497676 0.0005974770628 0.0005996415596 9.70808844e-07  
-   105          2    -23.69060481    -23.689825      0.0003899065755 0.0008774617579 0.0008800215906 1.681761199e-06 
-   106          2    -23.69149834    -23.690562      0.0004681676    0.0008527074936 0.0008560011682 1.11226924e-06  
-   107          2    -23.69145561    -23.690622      0.0004168050595 0.0008363624298 0.0008390017878 8.930611273e-07 
-   108          2    -23.68965306    -23.688764      0.0004445297309 0.0008936263738 0.0008910185183 1.309339573e-06 
-   109          2    -23.69077552    -23.690011      0.0003822592712 0.0006203793746 0.0006194287691 3.133550229e-07 
-   110          2    -23.68867102    -23.687696      0.0004875100015 0.001086068328  0.001087589996  1.327020171e-06 
-   111          2    -23.69172933    -23.691019      0.0003551646935 0.000852013148  0.0008540035129 9.847230007e-07 
-   112          2    -23.68991099    -23.689025      0.000442996005  6.46227386e-07  0               2.557212911e-07 
-   113          2    -23.69080506    -23.689952      0.0004265318142 7.012777671e-07 0               2.758977769e-07 
-   114          2    -23.69152793    -23.69061       0.0004589654148 0.0008542966264 0.0008580011655 1.338482046e-06 
-   115          2    -23.69153556    -23.690595      0.0004702783823 0.000867974804  0.0008680069124 6.687384672e-07 
-   116          2    -23.69117399    -23.690231      0.000471493636  0.0005924023762 0.0005925892338 1.259776007e-07 
-   117          2    -23.69139497    -23.690469      0.0004629856458 0.0008486906688 0.0008500294113 6.344879116e-07 
-   118          2    -23.69122801    -23.690482      0.0003730070077 0.0008734801582 0.0008740102974 2.172190141e-07 
-   119          2    -23.69055118    -23.689613      0.0004690919274 0.0008237358825 0.0008320192305 2.927942421e-06 
-   120          2    -23.68847553    -23.687426      0.0005247657372 0.001093739709  0.00109577735   8.307823424e-07 
-   121          2    -23.69041353    -23.689562      0.000425762889  0.0006210724415 0.0006265237426 1.574752432e-06 
-   122          2    -23.69137916    -23.6904        0.0004895814578 3.712921801e-07 0               1.509058252e-07 
-   123          2    -23.69152029    -23.690561      0.0004796427403 0.0005964911748 0.0005982273815 1.201511775e-06 
-   124          2    -23.69012377    -23.689107      0.0005083837539 0.0008124995989 0.0008180073349 1.97846325e-06  
-   125          2    -23.69112303    -23.690145      0.000489014125  0.0008742245309 0.0008740766557 1.981010569e-06 
-   126          2    -23.6913827     -23.690482      0.00045035056   0.0005944563316 0.0005939983165 2.227151791e-07 
-   127          2    -23.69071568    -23.689864      0.0004258388591 0.0008855411376 0.0008860124153 7.974985004e-07 
-# Elastic_FCC.xyz
-  config   # atoms      energy        DFT energy     energy error     force          DFT force       force error
-   128          4    -46.43709855    -46.437936      0.0002093617328 0.0008950059332 0.001265949446  0.0001464529791 
-   129          4    -46.4407039     -46.438504      0.0005499744469 0.0009975948265 0.001492549497  0.0001384062515 
-   130          4    -46.43497365    -46.436378      0.0003510867184 0.0005521282525 0.000810592376  9.989141969e-05 
-   131          4    -46.44077415    -46.441551      0.0001942123898 0.001132197907  0.001283675193  6.296966657e-05 
-   132          4    -46.41517164    -46.416957      0.0004463408133 0.000917990147  0.001186145859  8.226324971e-05 
-   133          4    -46.43849879    -46.440495      0.0004990529713 0.001000780113  0.001212440514  6.935590465e-05 
-   134          4    -46.43777706    -46.437972      4.873595839e-05 0.001389269665  0.002358226452  0.0002414827518 
-   135          4    -46.44772061    -46.44586       0.0004651524929 0.00136379307   0.002033949852  0.0001874009366 
-   136          4    -46.43566097    -46.435744      2.075858871e-05 0.0009531675039 0.001690849491  0.0002499304712 
-   137          4    -46.4397151     -46.438209      0.0003765248409 0.0008871611703 0.001160049999  6.827992039e-05 
-   138          4    -46.42609455    -46.42629       4.886349894e-05 0.0005556350766 0.0005297018029 1.21651498e-05  
-   139          4    -46.44149051    -46.443301      0.0004526223375 0.001132510738  0.001818421568  0.0001734412988 
-   140          4    -46.43896893    -46.439002      8.267473937e-06 0.001179879164  0.001416973535  6.937478941e-05 
-   141          4    -46.43123555    -46.432438      0.0003006112875 0.001147766739  0.001010469198  6.008540236e-05 
-   142          4    -46.41017485    -46.412654      0.0006197883649 0.001371501311  0.001801959766  0.0001610014112 
-   143          4    -46.44246774    -46.443231      0.0001908144167 0.0008879088126 0.001691590967  0.0001867981938 
-   144          4    -46.43057135    -46.431513      0.0002354128564 0.001455115574  0.001680544852  7.970584502e-05 
-   145          4    -46.43314849    -46.435608      0.0006148766383 0.000895665005  0.0009593039143 1.661569891e-05 
-   146          4    -46.43895751    -46.437689      0.0003171270659 0.001001644887  0.001217708504  8.864745791e-05 
-   147          4    -46.4271122     -46.428447      0.0003336990143 0.001053852574  0.002060081552  0.0002791878204 
-   148          4    -46.43182739    -46.432255      0.000106902789  0.0007125255966 0.0006274201144 7.371627608e-05 
-   149          4    -46.44177161    -46.442315      0.0001358463057 0.001140463867  0.002424436842  0.0003371037421 
-   150          4    -46.43717254    -46.436613      0.000139884251  0.0005515470124 0.0005321240457 4.25980675e-05  
-   151          4    -46.43004027    -46.430825      0.0001961823592 0.001008902912  0.001399987143  0.0001075255834 
-   152          4    -46.43208405    -46.43312       0.0002589881882 0.0005518528033 0.0007272771136 5.274203147e-05 
-   153          4    -46.43371444    -46.434347      0.000158140244  0.0008969169177 0.001284451634  0.000116451331  
-   154          4    -46.42879982    -46.430573      0.0004432948912 0.0009069765322 0.001315746176  0.0001014266222 
-   155          4    -46.44729799    -46.445665      0.0004082485341 0.001210137892  0.00180789159   0.0001638465464 
-   156          4    -46.43544342    -46.435898      0.0001136447769 0.0008978231434 0.001869300939  0.0002335504461 
-   157          4    -46.44021163    -46.442107      0.0004738424917 0.0007064270827 0.0006020930161 3.471655618e-05 
-   158          4    -46.43498956    -46.434432      0.0001393896227 0.0009533481605 0.001092982159  7.242855265e-05 
-   159          4    -46.43803608    -46.436308      0.0004320210529 0.001263659168  0.001839150891  0.0001727461868 
-   160          4    -46.42268734    -46.423938      0.0003126642441 0.001014412719  0.001463463016  0.0001717552709 
-   161          4    -46.42662921    -46.428115      0.0003714482928 0.0007136207063 0.0008584497656 6.405723837e-05 
-   162          4    -46.42531434    -46.4269        0.0003964160099 0.001206355349  0.001845719914  0.0002046485876 
-   163          4    -46.42224822    -46.421142      0.00027655517   0.001156356408  0.001309150106  4.994079618e-05 
-   164          4    -46.4302643     -46.432233      0.0004921743842 0.0007882966199 0.0007253109678 2.466489974e-05 
-   165          4    -46.43017473    -46.429408      0.0001916835518 0.000899021915  0.001068327665  6.208651635e-05 
-   166          4    -46.44541887    -46.445145      6.846642975e-05 0.001028604344  0.001776038288  0.0001975509563 
-   167          4    -46.43410132    -46.435868      0.0004416698523 0.00126629641   0.002376074704  0.0003279007933 
-   168          4    -46.43919494    -46.439663      0.0001170158831 0.0005441672792 0.001119403413  0.0001039537827 
-   169          4    -46.42584101    -46.428287      0.0006114968909 0.001286554794  0.001277000392  3.606396056e-05 
-   170          4    -46.42254993    -46.424584      0.000508517271  0.0007166928246 0.0008032957114 3.058246984e-05 
-   171          4    -46.41053526    -46.413045      0.0006274344802 0.001077488731  0.001248322074  4.395073797e-05 
-   172          4    -46.43440112    -46.436994      0.0006482191497 0.0009567631962 0.001331939188  0.0001491134491 
-   173          4    -46.44377744    -46.443604      4.335911262e-05 0.0009956173287 0.001177046303  8.761456142e-05 
-   174          4    -46.44028269    -46.439718      0.0001411716593 9.067044161e-07 0               2.475504855e-07 
-   175          4    -46.43723548    -46.435527      0.0004271206705 0.001133620344  0.0009338393866 8.014312499e-05 
-   176          4    -46.43396161    -46.434787      0.0002063465503 0.001150111339  0.00117329195   4.934565354e-05 
-   177          4    -46.43612253    -46.434929      0.0002983823621 0.001267526966  0.001349491756  5.093502218e-05 
-   178          4    -46.42638491    -46.426499      2.852244117e-05 0.001164859691  0.001248937949  4.347949244e-05 
-   179          4    -46.43717201    -46.437025      3.675245971e-05 0.0007725496777 0.000938418883  6.831038049e-05 
-   180          4    -46.4281895     -46.428937      0.0001868757356 0.001151243959  0.001286352984  4.994282406e-05 
-   181          4    -46.44116364    -46.442516      0.0003380892793 0.0007032387465 0.00094855469   0.0001088604201 
-   182          4    -46.42978258    -46.428736      0.0002616440103 0.001009629916  0.001424321593  0.0001089615662 
-   183          4    -46.43305551    -46.433359      7.587361447e-05 0.001156682853  0.001276381604  4.128766832e-05 
-   184          4    -46.44006475    -46.438799      0.0003164382753 0.0007752996065 0.0008186940821 3.548756745e-05 
-   185          4    -46.44169053    -46.441993      7.561864672e-05 0.0008970969052 0.001887735151  0.0002223397932 
-   186          4    -46.43727222    -46.439033      0.0004401954936 0.0007708721088 0.000821568013  4.107007018e-05 
-   187          4    -46.43632517    -46.436967      0.0001604574289 0.001052390296  0.001482323514  0.0001388091482 
-   188          4    -46.42718259    -46.427245      1.560352526e-05 0.001072419721  0.001293885621  7.709435507e-05 
-   189          4    -46.43874841    -46.438046      0.0001756024201 0.001260671216  0.001627288542  0.0001002074435 
-   190          4    -46.41877429    -46.420083      0.0003271768634 0.00142160315   0.002395244873  0.0003233098312 
-   191          4    -46.44621445    -46.445247      0.0002418615665 0.0009904374428 0.001219330964  5.687306262e-05 
-   192          4    -46.44511464    -46.446044      0.0002323410927 0.0008790838348 0.001305329077  0.0001107509197 
-   193          4    -46.43564394    -46.434472      0.0002929851777 0.000890378693  0.0008323340675 4.743679034e-05 
-   194          4    -46.44317175    -46.44458       0.0003520619573 0.0007034014662 0.0009744208536 5.172015881e-05 
-   195          4    -46.44087095    -46.441776      0.0002262624122 0.00113922313   0.001339231869  8.765052415e-05 
-   196          4    -46.43719326    -46.436389      0.0002010659177 0.001277508928  0.001786741168  0.0001303767454 
-   197          4    -46.44563996    -46.446416      0.0001940097871 0.0007007387602 0.0006588778339 5.645487424e-05 
-   198          4    -46.44980864    -46.449806      6.606823266e-07 0.001232826529  0.002135055034  0.0002384857832 
-   199          4    -46.42466674    -46.427189      0.0006305654832 0.001011828255  0.001050788276  2.797047454e-05 
-   200          4    -46.42588993    -46.427857      0.000491766418  0.001010915484  0.001487666629  0.0001398462887 
-   201          4    -46.44273693    -46.44004       0.0006742317456 0.0007050795233 0.000757202747  2.506458135e-05 
-   202          4    -46.43659247    -46.437214      0.0001553829854 0.0008924045914 0.001505586265  0.0001475571029 
-   203          4    -46.42189527    -46.422628      0.0001831835233 0.0009120248848 0.001601713458  0.0002207350143 
-   204          4    -46.44387014    -46.443535      8.378431277e-05 0.001253187495  0.001590304373  0.0001006147174 
-   205          4    -46.4386991     -46.439922      0.0003057254875 0.001138308324  0.001530493385  0.0001018467819 
-   206          4    -46.43732669    -46.437675      8.707637653e-05 0.00144833639   0.002440246094  0.0003149341193 
-   207          4    -46.44459348    -46.445558      0.0002411303465 0.0008716893522 0.00113392416   7.56134454e-05  
-   208          4    -46.43888136    -46.439106      5.615896373e-05 0.001259801268  0.001830731002  0.0001709222499 
-   209          4    -46.44452218    -46.443073      0.000362294488  0.0005355233492 0.0005766870902 1.79131844e-05  
-   210          4    -46.44072829    -46.4397        0.0002570727366 0.0008912594074 0.001204174406  7.190949652e-05 
-   211          4    -46.43632905    -46.436374      1.123701302e-05 0.00100454144   0.001461656594  0.0001640759619 
-   212          4    -46.42622449    -46.426557      8.312836801e-05 0.0009090508417 0.001359624213  9.618645017e-05 
-   213          4    -46.43334095    -46.434009      0.0001670117853 0.001064727099  0.001391131194  0.0001118380718 
-   214          4    -46.43528491    -46.436262      0.0002442735765 0.001381671175  0.002503347159  0.0002862586192 
-   215          4    -46.43302209    -46.434505      0.0003707286996 0.001050895795  0.001041637173  1.894959196e-05 
-   216          4    -46.43866543    -46.438768      2.564354619e-05 0.001038218613  0.001098285027  4.514351427e-05 
-   217          4    -46.43867092    -46.440254      0.000395771139  0.0005510961745 0.0006069892915 4.783705107e-05 
-   218          4    -46.42481603    -46.42286       0.0004890086715 0.0005673661918 0.0007365242698 6.506184883e-05 
-   219          4    -46.41707211    -46.418078      0.0002514715464 0.001292943265  0.002028412187  0.0002017017408 
-   220          4    -46.44058128    -46.440513      1.706961588e-05 0.0008917162415 0.001158189967  9.459271337e-05 
-   221          4    -46.40786735    -46.409824      0.000489161666  0.000915995593  0.001759573812  0.0002027400318 
-   222          4    -46.44176165    -46.440329      0.0003581615225 0.0007050784001 0.0009534044263 7.330945846e-05 
-   223          4    -46.43764613    -46.43773       2.096761683e-05 0.000774718051  0.000926180328  6.358620287e-05 
-   224          4    -46.41646676    -46.416525      1.456068592e-05 0.0007183862165 0.0007573664899 3.367541267e-05 
-   225          4    -46.44086814    -46.440293      0.0001437843048 0.0008909024924 0.0007725386722 2.803785114e-05 
-   226          4    -46.44027213    -46.43839       0.0004705337314 0.000707862011  0.0005612022808 3.305821092e-05 
-   227          4    -46.44117428    -46.438916      0.0005645706045 0.0008843758872 0.001650878554  0.0001728226219 
-# GSF_110.xyz
-  config   # atoms      energy        DFT energy     energy error     force          DFT force       force error
-   228         24    -278.9717069    -279.068761     0.004043919984  1.716820818     1.756353161     0.02195804808   
-   229         24    -279.8354387    -279.784296     0.002130947227  0.8360148085    0.9057668891    0.02306494198   
-   230         24    -279.920921     -279.901657     0.0008026661363 0.2958425997    0.001565946359  0.01411644584   
-   231         24    -279.6113309    -279.584238     0.001128870276  1.136927478     1.035572248     0.0268109436    
-   232         24    -279.8354404    -279.784283     0.002131557004  0.8360112083    0.9056396189    0.02305363685   
-   233         24    -279.302435     -279.302158     1.154096848e-05 1.736732738     1.771965137     0.03376130194   
-   234         24    -279.5958843    -279.55564      0.001676844981  1.457718936     1.405626506     0.02601748107   
-   235         24    -279.1575825    -279.246939     0.003723187357  0.7701803397    0.4813964151    0.04047323625   
-   236         24    -279.3024375    -279.302157     1.168852836e-05 1.736736025     1.771953347     0.03376039536   
-   237         24    -279.1575946    -279.246935     0.003722518226  0.7692677843    0.4809484798    0.04044520421   
-   238         24    -279.9208868    -279.896025     0.001035907873  0.2963184571    0.01060549839   0.01410249844   
-   239         24    -279.6115695    -279.584237     0.001138852664  1.13770573      1.035836121     0.02686761528   
-   240         24    -279.064529     -279.124427     0.002495750967  1.76375665      1.809545887     0.03536482035   
-   241         24    -279.3562359    -279.379366     0.000963755899  1.070359933     0.8982692706    0.03586365384   
-   242         24    -279.3561337    -279.37937      0.0009681791432 1.070187041     0.898081355     0.03582334182   
-   243         24    -279.0645273    -279.124427     0.002495818902  1.763753116     1.809523374     0.03536507377   
-   244         24    -279.920921     -279.901657     0.0008026661364 0.295842601     0.001570374478  0.01411415473   
-   245         24    -279.835369     -279.79264      0.001780376182  0.7694168746    0.8392614852    0.02365583077   
-   246         24    -279.9208868    -279.896025     0.001035907873  0.2963184557    0.01060243293   0.01410273421   
-   247         24    -279.0819585    -279.206496     0.005189061107  0.548788431     0.005326518563  0.03225764062   
-   248         24    -279.5958869    -279.55564      0.001676956181  1.457719116     1.4056319       0.02601845486   
-   249         24    -279.8353874    -279.79264      0.001781141415  0.7694021079    0.8392625708    0.0236575616    
-# GSF_112.xyz
-  config   # atoms      energy        DFT energy     energy error     force          DFT force       force error
-   250         30    -345.1958147    -345.175835     0.0006659888828 1.417827685     1.057395322     0.04924259711   
-   251         30    -346.4091654    -346.361714     0.001581712645  1.014644886     1.220284939     0.04659093523   
-   252         30    -345.9623042    -345.795524     0.005559340233  1.678459906     2.112860875     0.06265040874   
-   253         30    -345.1047773    -345.164602     0.001994157897  1.817583015     1.765832199     0.05258058387   
-   254         30    -346.5687925    -346.593523     0.0008243492414 0.5266160053    0.01148867129   0.03755504848   
-   255         30    -346.4165137    -346.396186     0.0006775885975 1.101956458     0.9954683928    0.04399110332   
-   256         30    -345.2521553    -345.319406     0.00224168982   2.024011434     1.772040852     0.05936118376   
-   257         30    -345.5898528    -345.594794     0.0001647082757 2.048144835     1.516014157     0.06040121307   
-   258         30    -346.0297765    -345.98566      0.001470549283  1.767327791     1.406252265     0.05243702855   
-   259         30    -345.5053828    -345.383994     0.004046292585  1.336428571     0.963574308     0.05104895348   
-   260         30    -346.5686342    -346.582564     0.0004643258311 0.5264214865    0.0126740587    0.03760971825   
-   261         30    -345.4208872    -345.452139     0.001041727499  3.011665478     2.787719406     0.06345649484   
-   262         30    -346.5687922    -346.593523     0.000824358736  0.5266293188    0.01148834      0.03755660424   
-   263         30    -345.4303122    -345.281949     0.004945440141  1.947208063     1.873142686     0.05337069289   
-   264         30    -345.95932      -345.928661     0.001021967701  2.362723976     2.100874472     0.05002108374   
-   265         30    -345.0137677    -345.111657     0.003262976998  3.19378163      3.358068319     0.06536423133   
-   266         30    -346.4078756    -346.367123     0.001358420679  1.085591236     1.335797131     0.04639235845   
-   267         30    -346.5685864    -346.582565     0.0004659529893 0.5264879505    0.01254743735   0.03760890253   
-   268         30    -344.8663405    -344.91356      0.001573984549  2.930408919     3.441834403     0.06926998065   
-   269         30    -345.9709087    -345.836703     0.004473521714  1.391835251     1.608769148     0.0557054003    
-   270         30    -345.0229891    -344.984307     0.001289401895  2.372016819     2.542628782     0.05571749983   
-   271         30    -346.4089445    -346.393931     0.0005004501598 1.297845976     1.211680725     0.04319349672   
-# Liquid.xyz
-  config   # atoms      energy        DFT energy     energy error     force          DFT force       force error
-   272        100    -1105.559726    -1105.601723    0.0004199683753 30.70196346     31.39853886     0.2273901869    
-   273        100    -1099.629534    -1099.673012    0.0004347802829 31.98646736     32.03167218     0.2226202775    
-   274        100    -1121.43168     -1121.31506     0.001166195007  21.23863202     20.81076453     0.2037539309    
-# Surface.xyz
-  config   # atoms      energy        DFT energy     energy error     force          DFT force       force error
-   275         24    -279.9208871    -279.911828     0.0003774634676 0.2963192975    0.002753093533  0.01433131958   
-   276         48    -554.241479     -555.359452     0.02329110353   1.363109446     0.003020630398  0.0573825018    
-   277         40    -459.5808398    -459.216162     0.009116945293  3.33149843      5.0461364       0.07877996461   
-   278         40    -460.5932467    -461.144076     0.01377073163   0.8854479197    0.005582740008  0.03813349763   
-   279         24    -279.8214986    -279.635146     0.007764693427  0.982012045     1.288799837     0.01857540863   
-   280         30    -346.5687933    -346.592525     0.000791056775  0.5266154723    0.008446203407  0.03726637101   
-   281         30    -346.0051971    -345.744506     0.008689702509  2.266739618     3.124961367     0.06591070739   
-# Volume_A15.xyz
-  config   # atoms      energy        DFT energy     energy error     force          DFT force       force error
-   282          8    -67.00264003    -66.990732      0.001488503243  8.978495355e-15 0               1.554167674e-15 
-   283          8    -72.95775645    -72.957807      6.318335608e-06 6.173563626e-14 0               9.086337007e-15 
-   284          8    -94.15079079    -94.145745      0.0006307242955 1.257001279e-14 0               1.651353601e-15 
-   285          8    -94.55576971    -94.554682      0.0001359640227 7.864226848e-15 0               1.351609702e-15 
-   286          8    -79.41650989    -79.438363      0.002731638712  2.922311383e-14 0               4.6112564e-15   
-   287          8    -69.6319055     -69.627817      0.0005110626381 3.131450246e-15 0               5.512083845e-16 
-   288          8    -82.6140242     -82.604907      0.001139650038  1.015341342e-14 0               1.573105072e-15 
-   289          8    14.8871533      14.89048        0.0004158371788 2.179622647e-13 0               3.718594804e-14 
-   290          8    -94.35602701    -94.367599      0.001446498413  1.681327296e-14 0               2.430951383e-15 
-   291          8    -89.2494361     -89.248227      0.0001511372198 1.602695388e-14 0               2.27566808e-15  
-   292          8    -87.22359357    -87.211997      0.001449571359  5.891018761e-15 0               1.023486851e-15 
-   293          8    -93.64917633    -93.66897       0.002474209194  1.737070481e-15 0               2.726891929e-16 
-   294          8    -7.974970896    -7.989166       0.001774387948  5.346466786e-13 0               7.317740119e-14 
-   295          8    -84.99735697    -84.982834      0.001815371577  1.628985705e-15 0               2.68014777e-16  
-   296          8    -92.51696442    -92.536373      0.002426072159  3.702813287e-14 0               5.965135793e-15 
-   297          8    -26.79883523    -26.77612       0.002839403163  2.314654929e-13 0               3.768467838e-14 
-   298          8    -77.53738473    -77.544107      0.0008402842141 2.975839122e-15 0               5.1405639e-16   
-   299          8    -80.11476757    -80.114217      6.882064461e-05 9.414427891e-15 0               1.325473296e-15 
-   300          8    -42.12903262    -42.143041      0.001751047533  2.610061598e-13 0               3.565304919e-14 
-   301          8    -91.02990946    -91.040671      0.001345192241  8.368513177e-15 0               1.310872707e-15 
-   302          8    -84.50933121    -84.499231      0.001262526145  5.714110441e-14 0               1.066782658e-14 
-   303          8    -61.79844789    -61.825173      0.003340638518  6.62953849e-15  0               1.015391475e-15 
-   304          8    -91.13057644    -91.156873      0.003287069749  4.719369293e-15 0               6.76336609e-16  
-   305          8    -54.64916677    -54.658744      0.001197153514  1.464956394e-13 0               2.113576767e-14 
-   306          8    -72.27319255    -72.277255      0.0005078062019 8.658199332e-16 0               1.410908427e-16 
-   307          8    -74.9147183     -74.923334      0.001076962465  4.434219242e-15 0               6.615078855e-16 
-   308          8    -64.81833247    -64.798066      0.002533308735  3.748412002e-14 0               5.576268614e-15 
-   309          8    -93.03489726    -93.048342      0.001680592822  1.857310674e-14 0               2.604235054e-15 
-   310          8    -64.39098013    -64.38702       0.0004950167019 5.001001166e-15 0               5.722057666e-16 
-   311          8    -88.36401125    -88.352871      0.001392531574  1.47982807e-14  0               2.645507511e-15 
-# Volume_BCC.xyz
-  config   # atoms      energy        DFT energy     energy error     force          DFT force       force error
-   312          2    -16.76594323    -16.763625      0.0011591154    3.058627912e-16 0               7.979727989e-17 
-   313          2    16.31372699     16.314145       0.0002090027274 8.186542193e-13 0               2.624717573e-13 
-   314          2    -21.21034402    -21.209071      0.000636508568  6.029606478e-15 0               1.688464572e-15 
-   315          2    -15.7845968     -15.780524      0.002036397536  5.051396178e-14 0               1.863971217e-14 
-   316          2    -18.99841038    -19.002205      0.001897311189  3.70201696e-14  0               1.247006253e-14 
-   317          2    -22.6245193     -22.620568      0.001975650815  3.866866338e-15 0               1.424786215e-15 
-   318          2    4.098164527     4.096885        0.0006397634862 6.334293648e-14 0               2.151519703e-14 
-   319          2    56.26275599     56.26276        2.005221472e-06 2.247995559e-12 0               7.580021273e-13 
-   320          2    -22.58944012    -22.585113      0.002163562406  1.113168148e-15 0               3.747002708e-16 
-   321          2    -21.79724015    -21.795501      0.0008695760695 1.09344287e-15  0               3.700743415e-16 
-   322          2    33.11015633     33.110078       3.916354612e-05 4.904232742e-13 0               1.492139745e-13 
-   323          2    -20.88315873    -20.885998      0.001419634185  1.859416424e-15 0               7.401486831e-16 
-   324          2    -23.59568898    -23.601336      0.002823509954  1.486164289e-15 0               4.916167932e-16 
-   325          2    -23.20858071    -23.207313      0.0006338528204 8.900302643e-16 0               3.147520853e-16 
-   326          2    -19.89310507    -19.898089      0.002491965758  8.784897284e-16 0               3.064678141e-16 
-   327          2    -23.40543384    -23.405474      2.007854096e-05 9.04864091e-16  0               2.55004351e-16  
-   328          2    -4.783890314    -4.781324       0.00128315718   1.026901322e-13 0               2.670433319e-14 
-   329          2    -18.86311291    -18.864936      0.0009115426716 2.305551267e-16 0               7.864079758e-17 
-   330          2    -17.81642588    -17.813086      0.001669937839  1.716587549e-16 0               6.245004514e-17 
-   331          2    -11.19369732    -11.197201      0.001751842379  6.247077482e-14 0               2.245483891e-14 
-   332          2    -23.6830862     -23.696705      0.006809399945  1.843658888e-15 0               7.087971703e-16 
-# Volume_FCC.xyz
-  config   # atoms      energy        DFT energy     energy error     force          DFT force       force error
-   333          4    -19.07363592    -19.075994      0.0005895202867 4.838977351e-14 0               1.162785146e-14 
-   334          4    -34.87911157    -34.873619      0.001373142448  2.834773835e-16 0               5.955883934e-17 
-   335          4    -43.95312208    -43.950003      0.0007797711561 2.246784353e-15 0               4.928060275e-16 
-   336          4    -40.99484531    -40.991909      0.0007340763059 8.408019466e-15 0               2.017013582e-15 
-   337          4    -43.44688587    -43.453929      0.001760782795  1.105978561e-14 0               2.960654589e-15 
-   338          4    -42.69057259    -42.686077      0.001123896575  2.15077979e-15  0               5.053466326e-16 
-   339          4    -33.22567657    -33.224653      0.0002558935333 6.71927174e-16  0               1.601728009e-16 
-   340          4    -26.86518979    -26.862709      0.0006201969912 3.31529179e-14  0               7.652202346e-15 
-   341          4    -25.52095377    -25.519883      0.0002676922193 3.655453829e-16 0               7.199102425e-17 
-   342          4    3.462101367     3.463071        0.0002424081278 1.816025861e-13 0               4.023864575e-14 
-   343          4    -31.5932268     -31.59595       0.0006807997919 3.628185658e-16 0               8.557969148e-17 
-   344          4    -45.10086835    -45.100466      0.0001005873411 2.465692424e-15 0               5.323999453e-16 
-   345          4    -46.05341345    -46.052258      0.0002888629271 8.511696107e-16 0               1.9963776e-16   
-   346          4    -29.99832749    -30.001189      0.0007153784531 3.847020655e-16 0               1.014813233e-16 
-   347          4    -22.85257327    -22.8504        0.0005433170403 7.603433695e-16 0               2.026735261e-16 
-   348          4    -9.165925377    -9.164691       0.0003085942037 6.355991568e-14 0               1.496321874e-14 
-   349          4    -24.14844545    -24.150343      0.0004743875843 4.762376771e-16 0               9.887923813e-17 
-   350          4    -46.43546878    -46.426795      0.002168445654  2.389854689e-15 0               6.508104241e-16 
-   351          4    -28.45126723    -28.451145      3.055783253e-05 7.811231556e-15 0               2.246466901e-15 
-   352          4    40.34134283     40.341566       5.579164045e-05 4.392900751e-13 0               1.047052708e-13 
-   353          4    19.618876       19.617912       0.0002409995917 2.653013854e-13 0               4.82657932e-14  
-   354          4    -26.95747287    -26.954384      0.0007722170381 5.063966549e-16 0               1.225871256e-16 
-   355          4    -46.33491981    -46.323696      0.002805953551  3.211950954e-15 0               8.731441496e-16 
-   356          4    -45.83316791    -45.828947      0.001055227438  1.228572267e-14 0               3.512236798e-15 
-   357          4    -38.16058675    -38.16029       7.418651586e-05 1.457184241e-15 0               3.625572065e-16 
-   358          4    -32.91257363    -32.919741      0.001791843199  5.73065335e-14  0               1.529158744e-14 
-   359          4    -41.2675262     -41.272675      0.001287199354  7.138843467e-15 0               2.027950471e-15 
-   360          4    -39.74460494    -39.753322      0.002179265661  7.861049173e-16 0               1.651275908e-16 
-   361          4    -37.55548161    -37.547435      0.002011652753  1.155947671e-14 0               2.497062164e-15 
-   362          4    -36.53186908    -36.52595       0.001479769423  3.660718685e-16 0               9.51206706e-17  
-   363          4    -45.01550153    -45.016087      0.0001463673621 1.766214736e-15 0               4.760370339e-16 

examples/PACKAGES/pod/Ta_Quadratic/Ta_training_errors.pod

@@ -1,20 +0,0 @@
-**************** Begin of Error Analysis for the Training Data Set ****************
----------------------------------------------------------------------------------------------------
-        File         | # configs |  # atoms  | MAE energy  | RMSE energy | MAE force  | RMSE force
----------------------------------------------------------------------------------------------------
-Displaced_A15.xyz            9         576     0.000554      0.000680      0.066393      0.083014  
-Displaced_BCC.xyz            9         486     0.004724      0.005103      0.108253      0.139461  
-Displaced_FCC.xyz            9         432     0.001704      0.001900      0.077531      0.097471  
-Elastic_BCC.xyz            100         200     0.000444      0.000446      0.000001      0.000002  
-Elastic_FCC.xyz            100         400     0.000273      0.000327      0.000110      0.000163  
-GSF_110.xyz                 22         528     0.001852      0.002260      0.027303      0.044765  
-GSF_112.xyz                 22         660     0.001839      0.002404      0.051415      0.080350  
-Liquid.xyz                   3         300     0.000674      0.000758      0.217921      0.276109  
-Surface.xyz                  7         236     0.009115      0.011661      0.047949      0.105123  
-Volume_A15.xyz              30         240     0.001407      0.001693      0.000000      0.000000  
-Volume_BCC.xyz              21          42     0.001497      0.002077      0.000000      0.000000  
-Volume_FCC.xyz              31         124     0.000870      0.001139      0.000000      0.000000  
----------------------------------------------------------------------------------------------------
-All files                  363        4224     0.001053      0.002171      0.059051      0.106960  
----------------------------------------------------------------------------------------------------
-**************** End of Error Analysis for the Training Data Set ****************

examples/PACKAGES/pod/Ta_Quadratic/in.fitpod

@@ -1,5 +0,0 @@
-# Demonstrate fitpod for POD potential
-
-units metal
-fitpod Ta_param.pod Ta_data.pod
-

examples/PACKAGES/pod/Ta_Quadratic/log.4Jan23.fitpod.g++.1

@@ -1,114 +0,0 @@
-LAMMPS (22 Dec 2022)
-  using 1 OpenMP thread(s) per MPI task
-# Demonstrate fitpod for POD potential
-
-units metal
-fitpod Ta_param.pod Ta_data.pod
-Reading potential file Ta_param.pod with DATE: 2022-11-30
-**************** Begin of POD Potentials ****************
-species: Ta 
-periodic boundary conditions: 1 1 1
-inner cut-off radius: 1
-outer cut-off radius: 5
-bessel polynomial degree: 3
-inverse polynomial degree: 6
-one-body potential: 1
-two-body potential: 3 6 6
-three-body potential: 3 6 5 5
-four-body SNAP potential: 0 0
-quadratic POD potential: 1
-number of basis functions for one-body potential: 1
-number of basis functions for two-body potential: 6
-number of basis functions for three-body potential: 25
-number of basis functions for four-body potential: 0
-number of descriptors for one-body potential: 1
-number of descriptors for two-body potential: 6
-number of descriptors for three-body potential: 25
-number of descriptors for four-body potential: 0
-number of descriptors for quadratic POD potential: 150
-total number of descriptors for all potentials: 182
-**************** End of POD Potentials ****************
-
-**************** Begin of Data File ****************
-file format: extxyz
-file extension: xyz
-path to training data set: ../Ta/XYZ
-path to test data set: ../Ta/XYZ
-training fraction: 1
-test fraction: 1
-randomize training data set: 1
-randomize test data set: 1
-error analysis for training data set: 1
-error analysis for test data set: 0
-energy/force calculation for training data set: 0
-energy/force calculation for test data set: 0
-fitting weight for energy: 100
-fitting weight for force: 1
-fitting weight for stress: 0
-fitting regularization parameter: 1e-10
-**************** End of Data File ****************
-**************** Begin of Training Data Set ****************
----------------------------------------------------------------
-     data file     | number of configurations | number of atoms
----------------------------------------------------------------
- Displaced_A15.xyz |                 9        |         576
- Displaced_BCC.xyz |                 9        |         486
- Displaced_FCC.xyz |                 9        |         432
- Elastic_BCC.xyz   |               100        |         200
- Elastic_FCC.xyz   |               100        |         400
- GSF_110.xyz       |                22        |         528
- GSF_112.xyz       |                22        |         660
- Liquid.xyz        |                 3        |         300
- Surface.xyz       |                 7        |         236
- Volume_A15.xyz    |                30        |         240
- Volume_BCC.xyz    |                21        |          42
- Volume_FCC.xyz    |                31        |         124
----------------------------------------------------------------
-number of files: 12
-number of configurations in all files: 363
-number of atoms in all files: 4224
-minimum number of atoms: 2
-maximum number of atoms: 100
-**************** End of Training Data Set ****************
-**************** Begin of Memory Allocation ****************
-maximum number of atoms in periodic domain: 100
-maximum number of atoms in extended domain: 2700
-maximum number of neighbors in extended domain: 270000
-size of double memory: 223201
-size of int memory: 14709
-size of descriptor matrix: 182 x 182
-**************** End of Memory Allocation ****************
-**************** Begin of Least-Squares Fitting ****************
-Configuration: # 1
-Configuration: # 101
-Configuration: # 201
-Configuration: # 301
-**************** End of Least-Squares Fitting ****************
-**************** Begin of Error Calculation ****************
-Configuration: # 1
-Configuration: # 101
-Configuration: # 201
-Configuration: # 301
-**************** End of Error Calculation ****************
-**************** Begin of Error Analysis for the Training Data Set ****************
----------------------------------------------------------------------------------------------------
-        File         | # configs |  # atoms  | MAE energy  | RMSE energy | MAE force  | RMSE force
----------------------------------------------------------------------------------------------------
-Displaced_A15.xyz            9         576     0.000554      0.000680      0.066393      0.083014  
-Displaced_BCC.xyz            9         486     0.004724      0.005103      0.108253      0.139461  
-Displaced_FCC.xyz            9         432     0.001704      0.001900      0.077531      0.097471  
-Elastic_BCC.xyz            100         200     0.000444      0.000446      0.000001      0.000002  
-Elastic_FCC.xyz            100         400     0.000273      0.000327      0.000110      0.000163  
-GSF_110.xyz                 22         528     0.001852      0.002260      0.027303      0.044765  
-GSF_112.xyz                 22         660     0.001839      0.002404      0.051415      0.080350  
-Liquid.xyz                   3         300     0.000674      0.000758      0.217921      0.276109  
-Surface.xyz                  7         236     0.009115      0.011661      0.047949      0.105123  
-Volume_A15.xyz              30         240     0.001407      0.001693      0.000000      0.000000  
-Volume_BCC.xyz              21          42     0.001497      0.002077      0.000000      0.000000  
-Volume_FCC.xyz              31         124     0.000870      0.001139      0.000000      0.000000  
----------------------------------------------------------------------------------------------------
-All files                  363        4224     0.001053      0.002171      0.059051      0.106960  
----------------------------------------------------------------------------------------------------
-**************** End of Error Analysis for the Training Data Set ****************
-
-Total wall time: 0:00:01

examples/PACKAGES/pod/Ta_Quadratic/log.4Jan23.pod.g++.1

@@ -1,142 +0,0 @@
-LAMMPS (22 Dec 2022)
-  using 1 OpenMP thread(s) per MPI task
-# Demonstrate POD Ta potential
-
-# Initialize simulation
-
-variable nsteps index 100
-variable nrep equal 4
-variable a equal 3.316
-units           metal
-
-# generate the box and atom positions using a BCC lattice
-
-variable nx equal ${nrep}
-variable nx equal 4
-variable ny equal ${nrep}
-variable ny equal 4
-variable nz equal ${nrep}
-variable nz equal 4
-
-boundary        p p p
-
-lattice         bcc $a
-lattice         bcc 3.316
-Lattice spacing in x,y,z = 3.316 3.316 3.316
-region          box block 0 ${nx} 0 ${ny} 0 ${nz}
-region          box block 0 4 0 ${ny} 0 ${nz}
-region          box block 0 4 0 4 0 ${nz}
-region          box block 0 4 0 4 0 4
-create_box      1 box
-Created orthogonal box = (0 0 0) to (13.264 13.264 13.264)
-  1 by 1 by 1 MPI processor grid
-create_atoms    1 box
-Created 128 atoms
-  using lattice units in orthogonal box = (0 0 0) to (13.264 13.264 13.264)
-  create_atoms CPU = 0.000 seconds
-
-mass 1 180.88
-
-
-# POD potential
-pair_style pod
-pair_coeff * * Ta_param.pod Ta_coefficients.pod Ta
-Reading potential file Ta_param.pod with DATE: 2022-11-30
-**************** Begin of POD Potentials ****************
-species: Ta 
-periodic boundary conditions: 1 1 1
-inner cut-off radius: 1
-outer cut-off radius: 5
-bessel polynomial degree: 3
-inverse polynomial degree: 6
-one-body potential: 1
-two-body potential: 3 6 6
-three-body potential: 3 6 5 5
-four-body SNAP potential: 0 0
-quadratic POD potential: 1
-number of basis functions for one-body potential: 1
-number of basis functions for two-body potential: 6
-number of basis functions for three-body potential: 25
-number of basis functions for four-body potential: 0
-number of descriptors for one-body potential: 1
-number of descriptors for two-body potential: 6
-number of descriptors for three-body potential: 25
-number of descriptors for four-body potential: 0
-number of descriptors for quadratic POD potential: 150
-total number of descriptors for all potentials: 182
-**************** End of POD Potentials ****************
-
-
-# Setup output
-
-thermo          10
-thermo_modify norm yes
-
-# Set up NVE run
-
-timestep 0.5e-3
-neighbor 1.0 bin
-neigh_modify once no every 1 delay 0 check yes
-
-# Run MD
-
-velocity all create 300.0 4928459 loop geom
-fix 1 all nve
-run             ${nsteps}
-run             100
-Neighbor list info ...
-  update: every = 1 steps, delay = 0 steps, check = yes
-  max neighbors/atom: 2000, page size: 100000
-  master list distance cutoff = 6
-  ghost atom cutoff = 6
-  binsize = 3, bins = 5 5 5
-  1 neighbor lists, perpetual/occasional/extra = 1 0 0
-  (1) pair pod, perpetual
-      attributes: full, newton on
-      pair build: full/bin/atomonly
-      stencil: full/bin/3d
-      bin: standard
-Per MPI rank memory allocation (min/avg/max) = 3.082 | 3.082 | 3.082 Mbytes
-   Step          Temp          E_pair         E_mol          TotEng         Press     
-         0   300           -11.847697      0             -11.809222      13502.169    
-        10   296.47494     -11.847245      0             -11.809222      13529.584    
-        20   286.0918      -11.845913      0             -11.809222      13613.884    
-        30   269.42275     -11.843776      0             -11.809222      13759.746    
-        40   247.39423     -11.84095       0             -11.809222      13972.073    
-        50   221.23976     -11.837596      0             -11.809222      14253.202    
-        60   192.43252     -11.833901      0             -11.809222      14600.367    
-        70   162.59874     -11.830075      0             -11.809221      15004.156    
-        80   133.41531     -11.826332      0             -11.809221      15448.418    
-        90   106.49785     -11.82288       0             -11.809221      15911.638    
-       100   83.288219     -11.819903      0             -11.809221      16369.373    
-Loop time of 1.51781 on 1 procs for 100 steps with 128 atoms
-
-Performance: 2.846 ns/day, 8.432 hours/ns, 65.884 timesteps/s, 8.433 katom-step/s
-99.8% CPU use with 1 MPI tasks x 1 OpenMP threads
-
-MPI task timing breakdown:
-Section |  min time  |  avg time  |  max time  |%varavg| %total
----------------------------------------------------------------
-Pair    | 1.5172     | 1.5172     | 1.5172     |   0.0 | 99.96
-Neigh   | 0          | 0          | 0          |   0.0 |  0.00
-Comm    | 0.0002542  | 0.0002542  | 0.0002542  |   0.0 |  0.02
-Output  | 0.00013308 | 0.00013308 | 0.00013308 |   0.0 |  0.01
-Modify  | 0.00012159 | 0.00012159 | 0.00012159 |   0.0 |  0.01
-Other   |            | 0.0001446  |            |       |  0.01
-
-Nlocal:            128 ave         128 max         128 min
-Histogram: 1 0 0 0 0 0 0 0 0 0
-Nghost:            727 ave         727 max         727 min
-Histogram: 1 0 0 0 0 0 0 0 0 0
-Neighs:              0 ave           0 max           0 min
-Histogram: 1 0 0 0 0 0 0 0 0 0
-FullNghs:         7424 ave        7424 max        7424 min
-Histogram: 1 0 0 0 0 0 0 0 0 0
-
-Total # of neighbors = 7424
-Ave neighs/atom = 58
-Neighbor list builds = 0
-Dangerous builds = 0
-
-
-Total wall time: 0:00:01

examples/PACKAGES/pod/Ta_Quadratic/log.4Jan23.pod.g++.4

@@ -1,142 +0,0 @@
-LAMMPS (22 Dec 2022)
-  using 1 OpenMP thread(s) per MPI task
-# Demonstrate POD Ta potential
-
-# Initialize simulation
-
-variable nsteps index 100
-variable nrep equal 4
-variable a equal 3.316
-units           metal
-
-# generate the box and atom positions using a BCC lattice
-
-variable nx equal ${nrep}
-variable nx equal 4
-variable ny equal ${nrep}
-variable ny equal 4
-variable nz equal ${nrep}
-variable nz equal 4
-
-boundary        p p p
-
-lattice         bcc $a
-lattice         bcc 3.316
-Lattice spacing in x,y,z = 3.316 3.316 3.316
-region          box block 0 ${nx} 0 ${ny} 0 ${nz}
-region          box block 0 4 0 ${ny} 0 ${nz}
-region          box block 0 4 0 4 0 ${nz}
-region          box block 0 4 0 4 0 4
-create_box      1 box
-Created orthogonal box = (0 0 0) to (13.264 13.264 13.264)
-  1 by 2 by 2 MPI processor grid
-create_atoms    1 box
-Created 128 atoms
-  using lattice units in orthogonal box = (0 0 0) to (13.264 13.264 13.264)
-  create_atoms CPU = 0.000 seconds
-
-mass 1 180.88
-
-
-# POD potential
-pair_style pod
-pair_coeff * * Ta_param.pod Ta_coefficients.pod Ta
-Reading potential file Ta_param.pod with DATE: 2022-11-30
-**************** Begin of POD Potentials ****************
-species: Ta 
-periodic boundary conditions: 1 1 1
-inner cut-off radius: 1
-outer cut-off radius: 5
-bessel polynomial degree: 3
-inverse polynomial degree: 6
-one-body potential: 1
-two-body potential: 3 6 6
-three-body potential: 3 6 5 5
-four-body SNAP potential: 0 0
-quadratic POD potential: 1
-number of basis functions for one-body potential: 1
-number of basis functions for two-body potential: 6
-number of basis functions for three-body potential: 25
-number of basis functions for four-body potential: 0
-number of descriptors for one-body potential: 1
-number of descriptors for two-body potential: 6
-number of descriptors for three-body potential: 25
-number of descriptors for four-body potential: 0
-number of descriptors for quadratic POD potential: 150
-total number of descriptors for all potentials: 182
-**************** End of POD Potentials ****************
-
-
-# Setup output
-
-thermo          10
-thermo_modify norm yes
-
-# Set up NVE run
-
-timestep 0.5e-3
-neighbor 1.0 bin
-neigh_modify once no every 1 delay 0 check yes
-
-# Run MD
-
-velocity all create 300.0 4928459 loop geom
-fix 1 all nve
-run             ${nsteps}
-run             100
-Neighbor list info ...
-  update: every = 1 steps, delay = 0 steps, check = yes
-  max neighbors/atom: 2000, page size: 100000
-  master list distance cutoff = 6
-  ghost atom cutoff = 6
-  binsize = 3, bins = 5 5 5
-  1 neighbor lists, perpetual/occasional/extra = 1 0 0
-  (1) pair pod, perpetual
-      attributes: full, newton on
-      pair build: full/bin/atomonly
-      stencil: full/bin/3d
-      bin: standard
-Per MPI rank memory allocation (min/avg/max) = 3.062 | 3.062 | 3.062 Mbytes
-   Step          Temp          E_pair         E_mol          TotEng         Press     
-         0   300           -11.847697      0             -11.809222      13502.169    
-        10   296.47494     -11.847245      0             -11.809222      13529.584    
-        20   286.0918      -11.845913      0             -11.809222      13613.884    
-        30   269.42275     -11.843776      0             -11.809222      13759.746    
-        40   247.39423     -11.84095       0             -11.809222      13972.073    
-        50   221.23976     -11.837596      0             -11.809222      14253.202    
-        60   192.43252     -11.833901      0             -11.809222      14600.367    
-        70   162.59874     -11.830075      0             -11.809221      15004.156    
-        80   133.41531     -11.826332      0             -11.809221      15448.418    
-        90   106.49785     -11.82288       0             -11.809221      15911.638    
-       100   83.288219     -11.819903      0             -11.809221      16369.373    
-Loop time of 0.427448 on 4 procs for 100 steps with 128 atoms
-
-Performance: 10.106 ns/day, 2.375 hours/ns, 233.947 timesteps/s, 29.945 katom-step/s
-97.9% CPU use with 4 MPI tasks x 1 OpenMP threads
-
-MPI task timing breakdown:
-Section |  min time  |  avg time  |  max time  |%varavg| %total
----------------------------------------------------------------
-Pair    | 0.40622    | 0.40946    | 0.419      |   0.9 | 95.79
-Neigh   | 0          | 0          | 0          |   0.0 |  0.00
-Comm    | 0.0071192  | 0.016995   | 0.020439   |   4.4 |  3.98
-Output  | 0.00012904 | 0.0002071  | 0.00043132 |   0.0 |  0.05
-Modify  | 3.905e-05  | 4.8089e-05 | 5.5714e-05 |   0.0 |  0.01
-Other   |            | 0.0007341  |            |       |  0.17
-
-Nlocal:             32 ave          32 max          32 min
-Histogram: 4 0 0 0 0 0 0 0 0 0
-Nghost:            431 ave         431 max         431 min
-Histogram: 4 0 0 0 0 0 0 0 0 0
-Neighs:              0 ave           0 max           0 min
-Histogram: 4 0 0 0 0 0 0 0 0 0
-FullNghs:         1856 ave        1856 max        1856 min
-Histogram: 4 0 0 0 0 0 0 0 0 0
-
-Total # of neighbors = 7424
-Ave neighs/atom = 58
-Neighbor list builds = 0
-Dangerous builds = 0
-
-
-Total wall time: 0:00:00

potentials/Ta_coeff.pod

@@ -1,33 +1,33 @@
-POD_coefficients: 32
+model_coefficients: 32 0 0
--4.44242  
+-4.45745  
-4.10219   
+29.40034  
-2.36987   
+-13.69439 
-3.92184   
+-0.32907  
--0.83796  
+-0.14786  
--0.79457  
+-1.35221  
--0.26230  
+-0.59315  
--21.24294 
+-26.30409 
--15.38460 
+-33.37233 
--38.44056 
+162.42473 
-8.29872   
+144.67248 
--42.54514 
+-149.50021
-2.79976   
+1.78603   
-3.76109   
+2.49026   
-5.23499   
+-11.04768 
-0.04878   
+-11.14333 
-2.96006   
+12.40537  
-0.09101   
+0.48284   
--0.19257  
+0.39345   
--0.24326  
+-2.25812  
--0.16735  
+-1.38908  
-0.53738   
+1.31551   
-0.02236   
+0.02974   
--0.00154  
+-0.05094  
-0.02488   
+-0.21177  
--0.00565  
+0.12127   
-0.07672   
+0.23170   
--0.05894  
+0.02426   
--0.05604  
+-0.15305  
--0.12664  
+-0.10803  
-0.11723   
+0.25628   
-0.00262   
+0.01291   

potentials/Ta_param.pod

@@ -1,4 +1,3 @@
-# DATE: 2022-11-30 UNITS: metal CONTRIBUTOR: Ngoc Cuong Nguyen, exapde@gmail.com CITATION:  https://arxiv.org/abs/2209.02362
 # chemical element symbols
 species Ta
 
@@ -11,28 +10,37 @@ rin 1.0
 # outer cut-off radius
 rcut 5.0
 
+# use only for enviroment-adaptive potentials
+number_of_environment_clusters 1
+
+# principal_components of local descriptors
+number_of_principal_components 2
+
 # polynomial degrees for radial basis functions
 bessel_polynomial_degree 3
 inverse_polynomial_degree 6
 
-# one-body potential
-onebody 1
-
 # two-body linear POD potential
 twobody_number_radial_basis_functions 6
 
 # three-body linear POD potential
 threebody_number_radial_basis_functions 5
-threebody_number_angular_basis_functions 5
+threebody_angular_degree 4
 
-# four-body linear SNAP potential
+# four-body linear POD potential
-fourbody_snap_twojmax 0 
+fourbody_number_radial_basis_functions 0
+fourbody_angular_degree 0
 
-# quadratic POD potential
+# five-body linear POD potential
-quadratic_pod_potential 0
+fivebody_number_radial_basis_functions 0
+fivebody_angular_degree 0
+
+# six-body linear POD potential
+sixbody_number_radial_basis_functions 0
+sixbody_angular_degree 0
+
+# seven-body linear POD potential
+sevenbody_number_radial_basis_functions 0
+sevenbody_angular_degree 0
 
-# Add the following basename to the name of output files
-basename_for_output_files Ta
 
-# number of digits after the decimal point
-precision_for_pod_coefficients 5

src/.gitignore

@@ -109,6 +109,8 @@
 
 /pair_pod.cpp
 /pair_pod.h
+/eapod.cpp
+/eapod.h
 /fitpod_command.cpp
 /fitpod_command.h
 /mlpod.cpp
@@ -249,6 +251,14 @@
 /compute_grid.h
 /compute_grid_local.cpp
 /compute_grid_local.h
+/compute_pod_atom.cpp
+/compute_pod_atom.h
+/compute_pod_global.cpp
+/compute_pod_global.h
+/compute_pod_local.cpp
+/compute_pod_local.h
+/compute_podd_atom.cpp
+/compute_podd_atom.h
 /compute_sna_atom.cpp
 /compute_sna_atom.h
 /compute_snad_atom.cpp

src/Depend.sh

@@ -185,6 +185,10 @@ if (test $1 = "ML-PACE") then
   depend KOKKOS
 fi
 
+if (test $1 = "ML-POD") then
+  depend KOKKOS
+fi
+
 if (test $1 = "ML-SNAP") then
   depend ML-IAP
   depend KOKKOS

src/FEP/fix_adapt_fep.cpp

@@ -92,9 +92,9 @@ FixAdaptFEP::FixAdaptFEP(LAMMPS *lmp, int narg, char **arg) :
       adapt[nadapt].pstyle = utils::strdup(arg[iarg+1]);
       adapt[nadapt].pparam = utils::strdup(arg[iarg+2]);
       utils::bounds_typelabel(FLERR, arg[iarg+3], 1, atom->ntypes,
-                              adapt[nadapt].ilo, adapt[nadapt].ihi, error, lmp, Atom::ATOM);
+                              adapt[nadapt].ilo, adapt[nadapt].ihi, lmp, Atom::ATOM);
       utils::bounds_typelabel(FLERR, arg[iarg+4], 1, atom->ntypes,
-                              adapt[nadapt].jlo, adapt[nadapt].jhi, error, lmp, Atom::ATOM);
+                              adapt[nadapt].jlo, adapt[nadapt].jhi, lmp, Atom::ATOM);
 
       // switch i,j if i > j, if wildcards were not used
 
@@ -131,7 +131,7 @@ FixAdaptFEP::FixAdaptFEP(LAMMPS *lmp, int narg, char **arg) :
         chgflag = 1;
       } else error->all(FLERR,"Illegal fix adapt/fep command");
       utils::bounds_typelabel(FLERR, arg[iarg+2], 1, atom->ntypes,
-                              adapt[nadapt].ilo, adapt[nadapt].ihi, error, lmp, Atom::ATOM);
+                              adapt[nadapt].ilo, adapt[nadapt].ihi, lmp, Atom::ATOM);
       if (utils::strmatch(arg[iarg+3],"^v_")) {
         adapt[nadapt].var = utils::strdup(arg[iarg+3]+2);
       } else error->all(FLERR,"Illegal fix adapt/fep command");

src/GRANULAR/fix_pour.cpp

@@ -703,7 +703,7 @@ void FixPour::pre_exchange()
   // rebuild atom map
 
   if (atom->map_style != Atom::MAP_NONE) {
-    if (success) atom->map_init();
+    atom->map_init();
     atom->map_set();
   }
 

src/INTEL/fix_nh_intel.cpp

@@ -26,6 +26,7 @@
 #include "memory.h"
 #include "modify.h"
 #include "neighbor.h"
+#include "respa.h"
 #include "update.h"
 
 #include <cmath>
@@ -335,8 +336,13 @@ void FixNHIntel::reset_dt()
 
   // If using respa, then remap is performed in innermost level
 
-  if (utils::strmatch(update->integrate_style,"^respa"))
+  if (utils::strmatch(update->integrate_style,"^respa")) {
+    auto respa_ptr = dynamic_cast<Respa *>(update->integrate);
+    if (!respa_ptr) error->all(FLERR, "Failure to access Respa style {}", update->integrate_style);
+    nlevels_respa = respa_ptr->nlevels;
+    step_respa = respa_ptr->step;
     dto = 0.5*step_respa[0];
+  }
 
   if (pstat_flag)
     pdrag_factor = 1.0 - (update->dt * p_freq_max * drag / nc_pchain);

src/KOKKOS/Install.sh

@@ -358,6 +358,8 @@ action pair_multi_lucy_rx_kokkos.cpp pair_multi_lucy_rx.cpp
 action pair_multi_lucy_rx_kokkos.h pair_multi_lucy_rx.h
 action pair_pace_extrapolation_kokkos.cpp pair_pace_extrapolation.cpp
 action pair_pace_extrapolation_kokkos.h pair_pace_extrapolation.h
+action pair_pod_kokkos.cpp pair_pod.cpp
+action pair_pod_kokkos.h pair_pod.h
 action pair_pace_kokkos.cpp pair_pace.cpp
 action pair_pace_kokkos.h pair_pace.h
 action pair_reaxff_kokkos.cpp pair_reaxff.cpp

src/KOKKOS/pair_buck_kokkos.cpp

@@ -138,9 +138,7 @@ template<class DeviceType>
 template<bool STACKPARAMS, class Specialisation>
 KOKKOS_INLINE_FUNCTION
 F_FLOAT PairBuckKokkos<DeviceType>::
-compute_fpair(const F_FLOAT& rsq, const int& i, const int&j, const int& itype, const int& jtype) const {
+compute_fpair(const F_FLOAT &rsq, const int &, const int &, const int &itype, const int &jtype) const {
-  (void) i;
-  (void) j;
   const F_FLOAT r2inv = 1.0/rsq;
   const F_FLOAT r6inv = r2inv*r2inv*r2inv;
   const F_FLOAT r = sqrt(rsq);
@@ -157,9 +155,7 @@ template<class DeviceType>
 template<bool STACKPARAMS, class Specialisation>
 KOKKOS_INLINE_FUNCTION
 F_FLOAT PairBuckKokkos<DeviceType>::
-compute_evdwl(const F_FLOAT& rsq, const int& i, const int&j, const int& itype, const int& jtype) const {
+compute_evdwl(const F_FLOAT &rsq, const int &, const int &, const int &itype, const int &jtype) const {
-  (void) i;
-  (void) j;
   const F_FLOAT r2inv = 1.0/rsq;
   const F_FLOAT r6inv = r2inv*r2inv*r2inv;
   const F_FLOAT r = sqrt(rsq);

src/KOKKOS/pair_lj_class2_coul_cut_kokkos.cpp

@@ -155,10 +155,8 @@ template<class DeviceType>
 template<bool STACKPARAMS, class Specialisation>
 KOKKOS_INLINE_FUNCTION
 F_FLOAT PairLJClass2CoulCutKokkos<DeviceType>::
-compute_fpair(const F_FLOAT& rsq, const int& i, const int&j,
+compute_fpair(const F_FLOAT &rsq, const int &, const int &,
-              const int& itype, const int& jtype) const {
+              const int &itype, const int &jtype) const {
-  (void) i;
-  (void) j;
   const F_FLOAT r2inv = 1.0/rsq;
   const F_FLOAT rinv = sqrt(r2inv);
   const F_FLOAT r3inv = r2inv*rinv;
@@ -178,9 +176,9 @@ template<class DeviceType>
 template<bool STACKPARAMS, class Specialisation>
 KOKKOS_INLINE_FUNCTION
 F_FLOAT PairLJClass2CoulCutKokkos<DeviceType>::
-compute_fcoul(const F_FLOAT& rsq, const int& /*i*/, const int&j,
+compute_fcoul(const F_FLOAT &rsq, const int &/*i*/, const int &j,
-              const int& /*itype*/, const int& /*jtype*/,
+              const int &/*itype*/, const int &/*jtype*/,
-              const F_FLOAT& factor_coul, const F_FLOAT& qtmp) const {
+              const F_FLOAT &factor_coul, const F_FLOAT &qtmp) const {
   const F_FLOAT r2inv = 1.0/rsq;
   const F_FLOAT rinv = sqrt(r2inv);
   F_FLOAT forcecoul;

src/KOKKOS/pair_lj_class2_coul_long_kokkos.cpp

@@ -160,10 +160,8 @@ template<class DeviceType>
 template<bool STACKPARAMS, class Specialisation>
 KOKKOS_INLINE_FUNCTION
 F_FLOAT PairLJClass2CoulLongKokkos<DeviceType>::
-compute_fpair(const F_FLOAT& rsq, const int& i, const int&j,
+compute_fpair(const F_FLOAT &rsq, const int &, const int &,
-              const int& itype, const int& jtype) const {
+              const int &itype, const int &jtype) const {
-  (void) i;
-  (void) j;
   const F_FLOAT r2inv = 1.0/rsq;
   const F_FLOAT rinv = sqrt(r2inv);
   const F_FLOAT r3inv = r2inv*rinv;
@@ -183,9 +181,9 @@ template<class DeviceType>
 template<bool STACKPARAMS,  class Specialisation>
 KOKKOS_INLINE_FUNCTION
 F_FLOAT PairLJClass2CoulLongKokkos<DeviceType>::
-compute_fcoul(const F_FLOAT& rsq, const int& /*i*/, const int&j,
+compute_fcoul(const F_FLOAT &rsq, const int &/*i*/, const int &j,
-              const int& /*itype*/, const int& /*jtype*/,
+              const int &/*itype*/, const int &/*jtype*/,
-              const F_FLOAT& factor_coul, const F_FLOAT& qtmp) const {
+              const F_FLOAT &factor_coul, const F_FLOAT &qtmp) const {
   if (Specialisation::DoTable && rsq > tabinnersq) {
     union_int_float_t rsq_lookup;
     rsq_lookup.f = rsq;

src/KOKKOS/pair_lj_class2_kokkos.cpp

@@ -139,9 +139,7 @@ template<class DeviceType>
 template<bool STACKPARAMS, class Specialisation>
 KOKKOS_INLINE_FUNCTION
 F_FLOAT PairLJClass2Kokkos<DeviceType>::
-compute_fpair(const F_FLOAT& rsq, const int& i, const int&j, const int& itype, const int& jtype) const {
+compute_fpair(const F_FLOAT &rsq, const int &, const int &, const int &itype, const int &jtype) const {
-  (void) i;
-  (void) j;
   const F_FLOAT r2inv = 1.0/rsq;
   const F_FLOAT rinv = sqrt(r2inv);
   const F_FLOAT r3inv = r2inv*rinv;
@@ -159,9 +157,7 @@ template<class DeviceType>
 template<bool STACKPARAMS, class Specialisation>
 KOKKOS_INLINE_FUNCTION
 F_FLOAT PairLJClass2Kokkos<DeviceType>::
-compute_evdwl(const F_FLOAT& rsq, const int& i, const int&j, const int& itype, const int& jtype) const {
+compute_evdwl(const F_FLOAT &rsq, const int &, const int &, const int &itype, const int &jtype) const {
-  (void) i;
-  (void) j;
   const F_FLOAT r2inv = 1.0/rsq;
   const F_FLOAT rinv = sqrt(r2inv);
   const F_FLOAT r3inv = r2inv*rinv;

src/KOKKOS/pair_lj_cut_kokkos.cpp

@@ -133,9 +133,7 @@ template<class DeviceType>
 template<bool STACKPARAMS, class Specialisation>
 KOKKOS_INLINE_FUNCTION
 F_FLOAT PairLJCutKokkos<DeviceType>::
-compute_fpair(const F_FLOAT& rsq, const int& i, const int&j, const int& itype, const int& jtype) const {
+compute_fpair(const F_FLOAT &rsq, const int &, const int &, const int &itype, const int &jtype) const {
-  (void) i;
-  (void) j;
   const F_FLOAT r2inv = 1.0/rsq;
   const F_FLOAT r6inv = r2inv*r2inv*r2inv;
 
@@ -150,9 +148,7 @@ template<class DeviceType>
 template<bool STACKPARAMS, class Specialisation>
 KOKKOS_INLINE_FUNCTION
 F_FLOAT PairLJCutKokkos<DeviceType>::
-compute_evdwl(const F_FLOAT& rsq, const int& i, const int&j, const int& itype, const int& jtype) const {
+compute_evdwl(const F_FLOAT &rsq, const int &, const int &, const int &itype, const int &jtype) const {
-  (void) i;
-  (void) j;
   const F_FLOAT r2inv = 1.0/rsq;
   const F_FLOAT r6inv = r2inv*r2inv*r2inv;
 

src/KOKKOS/pair_lj_spica_kokkos.cpp

@@ -138,39 +138,13 @@ template<class DeviceType>
 template<bool STACKPARAMS, class Specialisation>
 KOKKOS_INLINE_FUNCTION
 F_FLOAT PairLJSPICAKokkos<DeviceType>::
-compute_fpair(const F_FLOAT& rsq, const int& i, const int&j, const int& itype, const int& jtype) const {
+compute_fpair(const F_FLOAT &rsq, const int &, const int &, const int &itype, const int &jtype) const {
-  (void) i;
-  (void) j;
   const F_FLOAT r2inv = 1.0/rsq;
   const int ljt = (STACKPARAMS?m_params[itype][jtype].lj_type:params(itype,jtype).lj_type);
 
   const F_FLOAT lj_1 =  (STACKPARAMS?m_params[itype][jtype].lj1:params(itype,jtype).lj1);
   const F_FLOAT lj_2 =  (STACKPARAMS?m_params[itype][jtype].lj2:params(itype,jtype).lj2);
 
-  /*if (ljt == LJ12_4) {
-
-    const F_FLOAT r4inv=r2inv*r2inv;
-    return r4inv*(lj_1*r4inv*r4inv - lj_2) * r2inv;
-
-  } else if (ljt == LJ9_6) {
-
-    const F_FLOAT r3inv = r2inv*sqrt(r2inv);
-    const F_FLOAT r6inv = r3inv*r3inv;
-    return r6inv*(lj_1*r3inv - lj_2) * r2inv;
-
-  } else if (ljt == LJ12_6) {
-
-    const double r6inv = r2inv*r2inv*r2inv;
-    return r6inv*(lj_1*r6inv - lj_2) * r2inv;
-
-  } else if (ljt == LJ12_5) {
-
-    const F_FLOAT r5inv = r2inv*r2inv*sqrt(r2inv);
-    const F_FLOAT r7inv = r5inv*r2inv;
-    return r5inv*(lj_1*r7inv - lj_2) * r2inv;
-
-  }
-  if (ljt!=LJ12_4 && ljt!=LJ9_6 && ljt!=LJ12_6 && ljt!=LJ12_5) return 0.0;*/
   const F_FLOAT r4inv=r2inv*r2inv;
   const F_FLOAT r6inv=r2inv*r4inv;
   const F_FLOAT a = ljt==LJ12_4?r4inv:(ljt==LJ12_5?r4inv*sqrt(r2inv):r6inv);
@@ -182,9 +156,7 @@ template<class DeviceType>
 template<bool STACKPARAMS, class Specialisation>
 KOKKOS_INLINE_FUNCTION
 F_FLOAT PairLJSPICAKokkos<DeviceType>::
-compute_evdwl(const F_FLOAT& rsq, const int& i, const int&j, const int& itype, const int& jtype) const {
+compute_evdwl(const F_FLOAT &rsq, const int &, const int &, const int &itype, const int &jtype) const {
-  (void) i;
-  (void) j;
   const F_FLOAT r2inv = 1.0/rsq;
   const int ljt = (STACKPARAMS?m_params[itype][jtype].lj_type:params(itype,jtype).lj_type);
 

src/KOKKOS/pair_morse_kokkos.cpp

@@ -140,9 +140,7 @@ template<class DeviceType>
 template<bool STACKPARAMS, class Specialisation>
 KOKKOS_INLINE_FUNCTION
 F_FLOAT PairMorseKokkos<DeviceType>::
-compute_fpair(const F_FLOAT& rsq, const int& i, const int&j, const int& itype, const int& jtype) const {
+compute_fpair(const F_FLOAT &rsq, const int &, const int &, const int &itype, const int &jtype) const {
-  (void) i;
-  (void) j;
   const F_FLOAT rr = sqrt(rsq);
   const F_FLOAT r0 = STACKPARAMS ? m_params[itype][jtype].r0 : params(itype,jtype).r0;
   const F_FLOAT d0 = STACKPARAMS ? m_params[itype][jtype].d0 : params(itype,jtype).d0;
@@ -162,9 +160,7 @@ template<class DeviceType>
 template<bool STACKPARAMS, class Specialisation>
 KOKKOS_INLINE_FUNCTION
 F_FLOAT PairMorseKokkos<DeviceType>::
-compute_evdwl(const F_FLOAT& rsq, const int& i, const int&j, const int& itype, const int& jtype) const {
+compute_evdwl(const F_FLOAT &rsq, const int &, const int &, const int &itype, const int &jtype) const {
-  (void) i;
-  (void) j;
   const F_FLOAT rr = sqrt(rsq);
   const F_FLOAT r0 = STACKPARAMS ? m_params[itype][jtype].r0 : params(itype,jtype).r0;
   const F_FLOAT d0 = STACKPARAMS ? m_params[itype][jtype].d0 : params(itype,jtype).d0;

src/KOKKOS/pair_pod_kokkos.h

@@ -0,0 +1,226 @@
+/* -*- c++ -*- ----------------------------------------------------------
+   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
+   https://www.lammps.org/, Sandia National Laboratories
+   LAMMPS development team: developers@lammps.org
+
+   Copyright (2003) Sandia Corporation.  Under the terms of Contract
+   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
+   certain rights in this software.  This software is distributed under
+   the GNU General Public License.
+
+   See the README file in the top-level LAMMPS directory.
+------------------------------------------------------------------------- */
+
+#ifdef PAIR_CLASS
+// clang-format off
+PairStyle(pod/kk,PairPODKokkos<LMPDeviceType>);
+PairStyle(pod/kk/device,PairPODKokkos<LMPDeviceType>);
+PairStyle(pod/kk/host,PairPODKokkos<LMPHostType>);
+// clang-format on
+#else
+
+// clang-format off
+#ifndef LMP_PAIR_POD_KOKKOS_H
+#define LMP_PAIR_POD_KOKKOS_H
+
+#include "pair_pod.h"
+#include "kokkos_type.h"
+#include "pair_kokkos.h"
+
+namespace LAMMPS_NS {
+
+template<class DeviceType>
+class PairPODKokkos : public PairPOD {
+ public:
+  typedef DeviceType device_type;
+  typedef ArrayTypes<DeviceType> AT;
+
+  PairPODKokkos(class LAMMPS *);
+  ~PairPODKokkos() override;
+
+  void compute(int, int) override;
+  void coeff(int, char **) override;
+  void init_style() override;
+  double init_one(int, int) override;
+
+  int inum, maxneigh;
+  int host_flag;
+
+  int eflag, vflag;
+  int neighflag;
+
+  typename AT::t_neighbors_2d d_neighbors;
+  typename AT::t_int_1d d_ilist;
+  typename AT::t_int_1d d_numneigh;
+
+  DAT::tdual_efloat_1d k_eatom;
+  DAT::tdual_virial_array k_vatom;
+  typename AT::t_efloat_1d d_eatom;
+  typename AT::t_virial_array d_vatom;
+
+  typename AT::t_x_array_randomread x;
+  typename AT::t_f_array f;
+  typename AT::t_int_1d_randomread type;
+
+  typedef Kokkos::DualView<F_FLOAT**, DeviceType> tdual_fparams;
+  tdual_fparams k_cutsq, k_scale;
+  typedef Kokkos::View<F_FLOAT**, DeviceType> t_fparams;
+  t_fparams d_cutsq, d_scale;
+  typename AT::t_int_1d d_map;
+
+  friend void pair_virial_fdotr_compute<PairPODKokkos>(PairPODKokkos*);
+
+  void grow(int, int);
+  void copy_from_pod_class(EAPOD *podptr);
+  void divideInterval(int *intervals, int N, int M);
+  int calculateNumberOfIntervals(int N, int intervalSize);
+  void grow_atoms(int Ni);
+  void grow_pairs(int Nij);
+
+  void allocate() override;
+  double memory_usage() override;
+
+  typedef Kokkos::View<int*, DeviceType> t_pod_1i;
+  typedef Kokkos::View<double*, DeviceType> t_pod_1d;
+//   typedef Kokkos::View<int**, DeviceType> t_pod_2i;
+//   typedef Kokkos::View<double**, DeviceType> t_pod_2d;
+//   typedef Kokkos::View<double**[3], DeviceType> t_pod_3d3;
+
+  int atomBlockSize;        // size of each atom block
+  int nAtomBlocks;          // number of atoms blocks
+  int atomBlocks[101];      // atom blocks
+  double comptime[100];
+  int timing;
+
+  int ni;            // number of atoms i in the current atom block
+  int nij;           // number of pairs (i,j) in the current atom block
+  int nimax;         // maximum number of atoms i
+  int nijmax;        // maximum number of pairs (i,j)
+
+  int nelements; // number of elements
+  int onebody;   // one-body descriptors
+  int besseldegree; // degree of Bessel functions
+  int inversedegree; // degree of inverse functions
+  int nbesselpars;  // number of Bessel parameters
+  int nCoeffPerElement; // number of coefficients per element = (nl1 + Mdesc*nClusters)
+  int ns;      // number of snapshots for radial basis functions
+  int nl1, nl2, nl3, nl4, nl23, nl33, nl34, nl44, nl;   // number of local descriptors
+  int nrbf2, nrbf3, nrbf4, nrbfmax;            // number of radial basis functions
+  int nabf3, nabf4;                            // number of angular basis functions
+  int K3, K4, Q4;                                  // number of monomials
+
+  // environmental variables
+  int nClusters; // number of environment clusters
+  int nComponents; // number of principal components
+  int Mdesc; // number of base descriptors
+
+  double rin;  // inner cut-off radius
+  double rcut; // outer cut-off radius
+  double rmax; // rcut - rin
+  double rcutsq;
+
+  t_pod_1d rij;         // (xj - xi) for all pairs (I, J)
+  t_pod_1d fij;         // force for all pairs (I, J)
+  t_pod_1d ei;          // energy for each atom I
+  t_pod_1i typeai;         // types of atoms I only
+  t_pod_1i numij;          // number of pairs (I, J) for each atom I
+  t_pod_1i idxi;           // storing linear indices of atom I for all pairs (I, J)
+  t_pod_1i ai;             // IDs of atoms I for all pairs (I, J)
+  t_pod_1i aj;             // IDs of atoms J for all pairs (I, J)
+  t_pod_1i ti;             // types of atoms I for all pairs (I, J)
+  t_pod_1i tj;             // types of atoms J for all pairs (I, J)
+
+  t_pod_1d besselparams;
+  t_pod_1d Phi;  // eigenvectors matrix ns x ns
+  t_pod_1d rbf;  // radial basis functions nij x nrbfmax
+  t_pod_1d rbfx; // x-derivatives of radial basis functions nij x nrbfmax
+  t_pod_1d rbfy; // y-derivatives of radial basis functions nij x nrbfmax
+  t_pod_1d rbfz; // z-derivatives of radial basis functions nij x nrbfmax
+  t_pod_1d abf;  // angular basis functions nij x K3
+  t_pod_1d abfx; // x-derivatives of angular basis functions nij x K3
+  t_pod_1d abfy; // y-derivatives of angular basis functions nij x K3
+  t_pod_1d abfz; // z-derivatives of angular basis functions nij x K3
+  t_pod_1d sumU; // sum of radial basis functions ni x K3 x nrbfmax x nelements
+  t_pod_1d forcecoeff; // force coefficients ni x K3 x nrbfmax x nelements
+  t_pod_1d Proj; // PCA Projection matrix
+  t_pod_1d Centroids; // centroids of the clusters
+  t_pod_1d bd;   // base descriptors ni x Mdesc
+  t_pod_1d cb;   // force coefficients for base descriptors ni x Mdesc
+  t_pod_1d pd;   // environment probability descriptors ni x (1 + nComponents + 3*nClusters)
+  t_pod_1d coefficients; // coefficients nCoeffPerElement x nelements
+  t_pod_1i pq3, pn3, pc3; // arrays to compute 3-body angular basis functions
+  t_pod_1i pa4, pb4, pc4; // arrays to compute 4-body angular basis functions
+  t_pod_1i ind33l, ind33r; // nl33
+  t_pod_1i ind34l, ind34r; // nl34
+  t_pod_1i ind44l, ind44r; // nl44
+  t_pod_1i elemindex;
+
+  void set_array_to_zero(t_pod_1d a, int N);
+
+  int NeighborCount(t_pod_1i, double, int, int);
+
+  void NeighborList(t_pod_1d l_rij, t_pod_1i l_numij,  t_pod_1i l_typeai, t_pod_1i l_idxi,
+    t_pod_1i l_ai, t_pod_1i l_aj, t_pod_1i l_ti, t_pod_1i l_tj, double l_rcutsq, int gi1, int Ni);
+
+  void radialbasis(t_pod_1d rbft, t_pod_1d rbftx, t_pod_1d rbfty, t_pod_1d rbftz,
+    t_pod_1d rij, t_pod_1d l_besselparams, double l_rin, double l_rmax, int l_besseldegree,
+    int l_inversedegree, int l_nbesselpars, int Nij);
+
+  void matrixMultiply(t_pod_1d a, t_pod_1d b, t_pod_1d c, int r1, int c1, int c2);
+
+  void angularbasis(t_pod_1d l_abf, t_pod_1d l_abfx, t_pod_1d l_abfy, t_pod_1d l_abfz,
+        t_pod_1d l_rij, t_pod_1i l_pq3, int l_K3, int N);
+
+  void radialangularsum(t_pod_1d l_sumU, t_pod_1d l_rbf, t_pod_1d l_abf, t_pod_1i l_tj,
+    t_pod_1i l_numij, const int l_nelements, const int l_nrbf3, const int l_K3, const int Ni, const int Nij);
+
+  void twobodydesc(t_pod_1d d2, t_pod_1d l_rbf, t_pod_1i l_idxi, t_pod_1i l_tj, int l_nrbf2, const int Ni, const int Nij);
+
+  void threebodydesc(t_pod_1d d3, t_pod_1d l_sumU, t_pod_1i l_pc3, t_pod_1i l_pn3,
+        int l_nelements, int l_nrbf3, int l_nabf3, int l_K3, const int Ni);
+
+  void fourbodydesc(t_pod_1d d4,  t_pod_1d l_sumU, t_pod_1i l_pa4, t_pod_1i l_pb4, t_pod_1i l_pc4,
+      int l_nelements, int l_nrbf3, int l_nrbf4, int l_nabf4, int l_K3, int l_Q4, int Ni);
+
+  void crossdesc(t_pod_1d d12, t_pod_1d d1, t_pod_1d d2, t_pod_1i ind1, t_pod_1i ind2, int n12, int Ni);
+
+  void crossdesc_reduction(t_pod_1d cb1, t_pod_1d cb2, t_pod_1d c12, t_pod_1d d1,
+        t_pod_1d d2, t_pod_1i ind1, t_pod_1i ind2, int n12, int Ni);
+  void blockatom_base_descriptors(t_pod_1d bd, int Ni, int Nij);
+  void blockatom_base_coefficients(t_pod_1d ei, t_pod_1d cb, t_pod_1d B, int Ni);
+  void blockatom_environment_descriptors(t_pod_1d ei, t_pod_1d cb, t_pod_1d B, int Ni);
+
+  void twobody_forces(t_pod_1d fij, t_pod_1d cb2, t_pod_1d l_rbfx, t_pod_1d l_rbfy, t_pod_1d l_rbfz,
+          t_pod_1i l_idxi, t_pod_1i l_tj, int l_nrbf2, const int Ni, const int Nij);
+  void threebody_forces(t_pod_1d fij, t_pod_1d cb3, t_pod_1d l_rbf, t_pod_1d l_rbfx,
+    t_pod_1d l_rbfy, t_pod_1d l_rbfz, t_pod_1d l_abf, t_pod_1d l_abfx, t_pod_1d l_abfy, t_pod_1d l_abfz,
+    t_pod_1d l_sumU, t_pod_1i l_idxi, t_pod_1i l_tj, t_pod_1i l_pc3, t_pod_1i l_pn3, t_pod_1i l_elemindex,
+    int l_nelements, int l_nrbf3, int l_nabf3, int l_K3, int Ni, int Nij);
+  void fourbody_forces(t_pod_1d fij, t_pod_1d cb4, t_pod_1d l_rbf, t_pod_1d l_rbfx, t_pod_1d l_rbfy,
+    t_pod_1d l_rbfz, t_pod_1d l_abf, t_pod_1d l_abfx, t_pod_1d l_abfy, t_pod_1d l_abfz, t_pod_1d l_sumU,
+    t_pod_1i l_idxi, t_pod_1i l_tj, t_pod_1i l_pa4, t_pod_1i l_pb4, t_pod_1i l_pc4,
+    int l_nelements, int l_nrbf3, int l_nrbf4, int l_nabf4, int l_K3, int l_Q4, int Ni, int Nij);
+
+  void threebody_forcecoeff(t_pod_1d fb3, t_pod_1d cb3, t_pod_1d l_sumU, t_pod_1i l_pc3,
+    t_pod_1i l_pn3, t_pod_1i l_elemindex, int l_nelements, int l_nrbf3, int l_nabf3, int l_K3, int Ni);
+
+  void fourbody_forcecoeff(t_pod_1d fb4, t_pod_1d cb4, t_pod_1d l_sumU, t_pod_1i l_pa4,
+    t_pod_1i l_pb4, t_pod_1i l_pc4, int l_nelements, int l_nrbf3, int l_nrbf4, int l_nabf4, int l_K3, int l_Q4, int Ni);
+
+  void allbody_forces(t_pod_1d fij, t_pod_1d l_forcecoeff, t_pod_1d l_rbf, t_pod_1d l_rbfx,
+    t_pod_1d l_rbfy, t_pod_1d l_rbfz, t_pod_1d l_abf, t_pod_1d l_abfx, t_pod_1d l_abfy, t_pod_1d l_abfz,
+    t_pod_1i l_idxi, t_pod_1i l_tj, int l_nelements, int l_nrbf3, int l_K3, int Nij);
+
+  void blockatom_energyforce(t_pod_1d l_ei, t_pod_1d l_fij, int Ni, int Nij);
+  void tallyenergy(t_pod_1d l_ei, int istart, int Ni);
+  void tallyforce(t_pod_1d l_fij, t_pod_1i l_ai, t_pod_1i l_aj, int Nij);
+  void tallystress(t_pod_1d l_fij, t_pod_1d l_rij, t_pod_1i l_ai, t_pod_1i l_aj, int Nij);
+
+  void savematrix2binfile(std::string filename, t_pod_1d d_A, int nrows, int ncols);
+  void saveintmatrix2binfile(std::string filename, t_pod_1i d_A, int nrows, int ncols);
+  void savedatafordebugging();
+};
+}    // namespace LAMMPS_NS
+
+#endif
+#endif

src/KOKKOS/pair_soft_kokkos.cpp

@@ -135,16 +135,14 @@ template<class DeviceType>
 template<bool STACKPARAMS, class Specialisation>
 KOKKOS_INLINE_FUNCTION
 F_FLOAT PairSoftKokkos<DeviceType>::
-compute_fpair(const F_FLOAT& rsq, const int& i, const int&j, const int& itype, const int& jtype) const {
+compute_fpair(const F_FLOAT& rsq, const int &, const int &, const int& itype, const int& jtype) const {
-  (void) i;
   const F_FLOAT r = sqrt(rsq);
   const F_FLOAT cut_ij = STACKPARAMS?m_params[itype][jtype].cut:params(itype,jtype).cut;
   const F_FLOAT prefactor_ij = STACKPARAMS?m_params[itype][jtype].prefactor:params(itype,jtype).prefactor;
   const F_FLOAT arg = MY_PI*r/cut_ij;
 
   F_FLOAT fpair = 0.0;
-  if (r > 0.0) fpair = prefactor_ij *
+  if (r > 0.0) fpair = prefactor_ij * sin(arg) * MY_PI/cut_ij/r;
-                 sin(arg) * MY_PI/cut_ij/r;
 
   return fpair;
 }
@@ -153,8 +151,7 @@ template<class DeviceType>
 template<bool STACKPARAMS, class Specialisation>
 KOKKOS_INLINE_FUNCTION
 F_FLOAT PairSoftKokkos<DeviceType>::
-compute_evdwl(const F_FLOAT& rsq, const int& i, const int&j, const int& itype, const int& jtype) const {
+compute_evdwl(const F_FLOAT& rsq, const int &, const int &, const int& itype, const int& jtype) const {
-  (void) i;
   const F_FLOAT r = sqrt(rsq);
   const F_FLOAT cut_ij = STACKPARAMS?m_params[itype][jtype].cut:params(itype,jtype).cut;
   const F_FLOAT prefactor_ij = STACKPARAMS?m_params[itype][jtype].prefactor:params(itype,jtype).prefactor;

src/KOKKOS/pair_table_kokkos.cpp

@@ -202,9 +202,7 @@ template<class DeviceType>
 template<bool STACKPARAMS, class Specialisation>
 KOKKOS_INLINE_FUNCTION
 F_FLOAT PairTableKokkos<DeviceType>::
-compute_fpair(const F_FLOAT& rsq, const int& i, const int&j, const int& itype, const int& jtype) const {
+compute_fpair(const F_FLOAT &rsq, const int &, const int &, const int &itype, const int &jtype) const {
-  (void) i;
-  (void) j;
   union_int_float_t rsq_lookup;
   double fpair;
   const int tidx = d_table_const.tabindex(itype,jtype);
@@ -236,9 +234,7 @@ template<class DeviceType>
 template<bool STACKPARAMS, class Specialisation>
 KOKKOS_INLINE_FUNCTION
 F_FLOAT PairTableKokkos<DeviceType>::
-compute_evdwl(const F_FLOAT& rsq, const int& i, const int&j, const int& itype, const int& jtype) const {
+compute_evdwl(const F_FLOAT &rsq, const int &, const int &, const int &itype, const int &jtype) const {
-  (void) i;
-  (void) j;
   double evdwl;
   union_int_float_t rsq_lookup;
   const int tidx = d_table_const.tabindex(itype,jtype);

src/KOKKOS/pair_yukawa_colloid_kokkos.cpp

@@ -216,10 +216,8 @@ template<class DeviceType>
 template<bool STACKPARAMS, class Specialisation>
 KOKKOS_INLINE_FUNCTION
 F_FLOAT PairYukawaColloidKokkos<DeviceType>::
-compute_fpair(const F_FLOAT& rsq, const int& i, const int&j,
+compute_fpair(const F_FLOAT &rsq, const int &i, const int &j,
-              const int& itype, const int& jtype) const {
+              const int &itype, const int &jtype) const {
-  (void) i;
-  (void) j;
   const F_FLOAT radi   = radius[i];
   const F_FLOAT radj   = radius[j];
   const F_FLOAT rr     = sqrt(rsq);
@@ -242,10 +240,8 @@ template<class DeviceType>
 template<bool STACKPARAMS, class Specialisation>
 KOKKOS_INLINE_FUNCTION
 F_FLOAT PairYukawaColloidKokkos<DeviceType>::
-compute_evdwl(const F_FLOAT& rsq, const int& i, const int&j,
+compute_evdwl(const F_FLOAT &rsq, const int &i, const int &j,
-              const int& itype, const int& jtype) const {
+              const int &itype, const int &jtype) const {
-  (void) i;
-  (void) j;
   const F_FLOAT radi   = radius[i];
   const F_FLOAT radj   = radius[j];
   const F_FLOAT rr     = sqrt(rsq);

src/KOKKOS/pair_yukawa_kokkos.cpp

@@ -215,10 +215,8 @@ template<class DeviceType>
 template<bool STACKPARAMS, class Specialisation>
 KOKKOS_INLINE_FUNCTION
 F_FLOAT PairYukawaKokkos<DeviceType>::
-compute_fpair(const F_FLOAT& rsq, const int& i, const int&j,
+compute_fpair(const F_FLOAT &rsq, const int &, const int &,
-              const int& itype, const int& jtype) const {
+              const int &itype, const int &jtype) const {
-  (void) i;
-  (void) j;
   const F_FLOAT rr     = sqrt(rsq);
   // Fetch the params either off the stack or from some mapped memory?
   const F_FLOAT aa     = STACKPARAMS ? m_params[itype][jtype].a
@@ -241,10 +239,8 @@ template<class DeviceType>
 template<bool STACKPARAMS, class Specialisation>
 KOKKOS_INLINE_FUNCTION
 F_FLOAT PairYukawaKokkos<DeviceType>::
-compute_evdwl(const F_FLOAT& rsq, const int& i, const int&j,
+compute_evdwl(const F_FLOAT &rsq, const int &, const int &,
-              const int& itype, const int& jtype) const {
+              const int &itype, const int &jtype) const {
-  (void) i;
-  (void) j;
   const F_FLOAT rr     = sqrt(rsq);
   const F_FLOAT aa     = STACKPARAMS ? m_params[itype][jtype].a
                                      : params(itype,jtype).a;

src/KOKKOS/pair_zbl_kokkos.cpp

@@ -184,9 +184,7 @@ template<class DeviceType>
 template<bool STACKPARAMS, class Specialisation>
 KOKKOS_INLINE_FUNCTION
 F_FLOAT PairZBLKokkos<DeviceType>::
-compute_fpair(const F_FLOAT& rsq, const int& i, const int&j, const int& itype, const int& jtype) const {
+compute_fpair(const F_FLOAT& rsq, const int &, const int &, const int &itype, const int &jtype) const {
-  (void) i;
-  (void) j;
   const F_FLOAT r = sqrt(rsq);
   F_FLOAT fpair = dzbldr(r, itype, jtype);
 
@@ -205,9 +203,7 @@ template<class DeviceType>
 template<bool STACKPARAMS, class Specialisation>
 KOKKOS_INLINE_FUNCTION
 F_FLOAT PairZBLKokkos<DeviceType>::
-compute_evdwl(const F_FLOAT& rsq, const int& i, const int&j, const int& itype, const int& jtype) const {
+compute_evdwl(const F_FLOAT &rsq, const int &, const int &, const int &itype, const int &jtype) const {
-  (void) i;
-  (void) j;
   const F_FLOAT r = sqrt(rsq);
   F_FLOAT evdwl = e_zbl(r, itype, jtype);
   evdwl += d_sw5(itype,jtype);

src/ML-POD/compute_pod_atom.cpp

@@ -0,0 +1,277 @@
+// clang-format off
+/* ----------------------------------------------------------------------
+   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
+   https://www.lammps.org/, Sandia National Laboratories
+   LAMMPS development team: developers@lammps.org
+
+   Copyright (2003) Sandia Corporation.  Under the terms of Contract
+   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
+   certain rights in this software.  This software is distributed under
+   the GNU General Public License.
+
+   See the README file in the top-level LAMMPS directory.
+------------------------------------------------------------------------- */
+
+#include "compute_pod_atom.h"
+
+#include "atom.h"
+#include "comm.h"
+#include "error.h"
+#include "force.h"
+#include "memory.h"
+#include "modify.h"
+#include "neigh_list.h"
+#include "neighbor.h"
+#include "pair.h"
+#include "update.h"
+
+#include <cstring>
+
+#include "eapod.h"
+
+using namespace LAMMPS_NS;
+
+enum { SCALAR, VECTOR, ARRAY };
+
+ComputePODAtom::ComputePODAtom(LAMMPS *lmp, int narg, char **arg) :
+    Compute(lmp, narg, arg), list(nullptr), podptr(nullptr), pod(nullptr), tmpmem(nullptr),
+    rij(nullptr), elements(nullptr), map(nullptr)
+{
+  int nargmin = 6;
+
+  if (narg < nargmin) error->all(FLERR, "Illegal compute {} command", style);
+  if (comm->nprocs > 1) error->all(FLERR, "compute command does not support multi processors");
+
+  std::string pod_file = std::string(arg[3]);      // pod input file
+  std::string coeff_file = std::string(arg[4]);    // coefficient input file
+  podptr = new EAPOD(lmp, pod_file, coeff_file);
+
+  int ntypes = atom->ntypes;
+  memory->create(map, ntypes + 1, "compute_pod_global:map");
+  map_element2type(narg - 5, arg + 5, podptr->nelements);
+
+  cutmax = podptr->rcut;
+
+  nmax = 0;
+  nijmax = 0;
+  pod = nullptr;
+  elements = nullptr;
+
+  size_peratom_cols = podptr->Mdesc * podptr->nClusters;
+  peratom_flag = 1;
+}
+
+/* ---------------------------------------------------------------------- */
+
+ComputePODAtom::~ComputePODAtom()
+{
+  memory->destroy(map);
+  memory->destroy(pod);
+  delete podptr;
+}
+
+/* ---------------------------------------------------------------------- */
+
+void ComputePODAtom::init()
+{
+  if (force->pair == nullptr)
+    error->all(FLERR,"Compute pod requires a pair style be defined");
+
+  if (cutmax > force->pair->cutforce)
+    error->all(FLERR,"Compute pod cutoff is longer than pairwise cutoff");
+
+  // need an occasional full neighbor list
+
+  neighbor->add_request(this, NeighConst::REQ_FULL | NeighConst::REQ_OCCASIONAL);
+
+  if (modify->get_compute_by_style("pod").size() > 1 && comm->me == 0)
+    error->warning(FLERR,"More than one compute pod");
+}
+
+
+/* ---------------------------------------------------------------------- */
+
+void ComputePODAtom::init_list(int /*id*/, NeighList *ptr)
+{
+  list = ptr;
+}
+
+/* ---------------------------------------------------------------------- */
+
+void ComputePODAtom::compute_peratom()
+{
+  invoked_peratom = update->ntimestep;
+
+  // grow pod array if necessary
+
+  if (atom->natoms > nmax) {
+    memory->destroy(pod);
+    nmax = atom->natoms;
+    int numdesc = podptr->Mdesc * podptr->nClusters;
+    memory->create(pod, nmax, numdesc,"sna/atom:sna");
+    array_atom = pod;
+  }
+
+  for (int i = 0; i < atom->natoms; i++)
+    for (int icoeff = 0; icoeff < size_peratom_cols; icoeff++) {
+      pod[i][icoeff] = 0.0;
+    }
+
+  // invoke full neighbor list (will copy or build if necessary)
+
+  neighbor->build_one(list);
+
+  double **x = atom->x;
+  int **firstneigh = list->firstneigh;
+  int *numneigh = list->numneigh;
+  int *type = atom->type;
+  int *ilist = list->ilist;
+  int inum = list->inum;
+  int nClusters = podptr->nClusters;
+  int Mdesc = podptr->Mdesc;
+  double rcutsq = podptr->rcut*podptr->rcut;
+
+  for (int ii = 0; ii < inum; ii++) {
+    int i = ilist[ii];
+    int jnum = numneigh[i];
+
+    // allocate temporary memory
+    if (nijmax < jnum) {
+      nijmax = MAX(nijmax, jnum);
+      podptr->free_temp_memory();
+      podptr->allocate_temp_memory(nijmax);
+    }
+
+    rij = &podptr->tmpmem[0];
+    tmpmem = &podptr->tmpmem[3*nijmax];
+    ai = &podptr->tmpint[0];
+    aj = &podptr->tmpint[nijmax];
+    ti = &podptr->tmpint[2*nijmax];
+    tj = &podptr->tmpint[3*nijmax];
+
+    // get neighbor list for atom i
+    lammpsNeighborList(x, firstneigh, atom->tag, type, numneigh, rcutsq, i);
+
+    if (nij > 0) {
+      // peratom base descriptors
+      double *bd = &podptr->bd[0];
+      double *bdd = &podptr->bdd[0];
+      podptr->peratombase_descriptors(bd, bdd, rij, tmpmem, tj, nij);
+
+      if (nClusters>1) {
+        // peratom env descriptors
+        double *pd = &podptr->pd[0];
+        double *pdd = &podptr->pdd[0];
+        podptr->peratomenvironment_descriptors(pd, pdd, bd, bdd, tmpmem, ti[0] - 1,  nij);
+        for (int k = 0; k < nClusters; k++)
+          for (int m = 0; m < Mdesc; m++) {
+            int mk = m + Mdesc*k;
+            pod[i][mk] = pd[k]*bd[m];
+          //   for (int n=0; n<nij; n++) {
+          //     int ain = 3*ai[n];
+          //     int ajn = 3*aj[n];
+          //     int nm = 3*n + 3*nij*m;
+          //     int nk = 3*n + 3*nij*k;
+          //     pod[1 + ain][imk] += bdd[0 + nm]*pd[k] + bd[m]*pdd[0+nk];
+          //     pod[2 + ain][imk] += bdd[1 + nm]*pd[k] + bd[m]*pdd[1+nk];
+          //     pod[3 + ain][imk] += bdd[2 + nm]*pd[k] + bd[m]*pdd[2+nk];
+          //     pod[1 + ajn][imk] -= bdd[0 + nm]*pd[k] + bd[m]*pdd[0+nk];
+          //     pod[2 + ajn][imk] -= bdd[1 + nm]*pd[k] + bd[m]*pdd[1+nk];
+          //     pod[3 + ajn][imk] -= bdd[2 + nm]*pd[k] + bd[m]*pdd[2+nk];
+          //   }
+          }
+      }
+      else {
+        for (int m = 0; m < Mdesc; m++) {
+         pod[i][m] = bd[m];
+        //  for (int n=0; n<nij; n++) {
+        //     int ain = 3*ai[n];
+        //     int ajn = 3*aj[n];
+        //     int nm = 3*n + 3*nij*m;
+        //     pod[1 + ain][im] += bdd[0 + nm];
+        //     pod[2 + ain][im] += bdd[1 + nm];
+        //     pod[3 + ain][im] += bdd[2 + nm];
+        //     pod[1 + ajn][im] -= bdd[0 + nm];
+        //     pod[2 + ajn][im] -= bdd[1 + nm];
+        //     pod[3 + ajn][im] -= bdd[2 + nm];
+        //   }
+        }
+      }
+    }
+  }
+}
+
+/* ----------------------------------------------------------------------
+   memory usage
+------------------------------------------------------------------------- */
+
+double ComputePODAtom::memory_usage()
+{
+  double bytes = 0.0;
+
+  return bytes;
+}
+
+void ComputePODAtom::lammpsNeighborList(double **x, int **firstneigh, tagint *atomid, int *atomtypes,
+                               int *numneigh, double rcutsq, int gi)
+{
+  nij = 0;
+  int itype = map[atomtypes[gi]] + 1;
+  int m = numneigh[gi];
+  ti[nij] = itype;
+  for (int l = 0; l < m; l++) {           // loop over each atom around atom i
+    int gj = firstneigh[gi][l];           // atom j
+    double delx = x[gj][0] - x[gi][0];    // xj - xi
+    double dely = x[gj][1] - x[gi][1];    // xj - xi
+    double delz = x[gj][2] - x[gi][2];    // xj - xi
+    double rsq = delx * delx + dely * dely + delz * delz;
+    if (rsq < rcutsq && rsq > 1e-20) {
+      rij[nij * 3 + 0] = delx;
+      rij[nij * 3 + 1] = dely;
+      rij[nij * 3 + 2] = delz;
+      ai[nij] = atomid[gi]-1;
+      aj[nij] = atomid[gj]-1;
+      ti[nij] = itype;
+      tj[nij] = map[atomtypes[gj]] + 1;
+      nij++;
+    }
+  }
+}
+
+void ComputePODAtom::map_element2type(int narg, char **arg, int nelements)
+{
+  int i,j;
+  const int ntypes = atom->ntypes;
+
+  // read args that map atom types to elements in potential file
+  // map[i] = which element the Ith atom type is, -1 if "NULL"
+  // nelements = # of unique elements
+  // elements = list of element names
+
+  if (narg != ntypes)
+    error->all(FLERR, "Number of element to type mappings does not match number of atom types");
+
+  if (elements) {
+    for (i = 0; i < nelements; i++) delete[] elements[i];
+    delete[] elements;
+  }
+  elements = new char*[ntypes];
+  for (i = 0; i < ntypes; i++) elements[i] = nullptr;
+
+  nelements = 0;
+  map[0] = -1;
+  for (i = 1; i <= narg; i++) {
+    std::string entry = arg[i-1];
+    if (entry == "NULL") {
+      map[i] = -1;
+      continue;
+    }
+    for (j = 0; j < nelements; j++)
+      if (entry == elements[j]) break;
+    map[i] = j;
+    if (j == nelements) {
+      elements[j] = utils::strdup(entry);
+      nelements++;
+    }
+  }
+}

src/ML-POD/compute_pod_atom.h

@@ -0,0 +1,61 @@
+/* -*- c++ -*- ----------------------------------------------------------
+   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
+   https://www.lammps.org/, Sandia National Laboratories
+   LAMMPS development team: developers@lammps.org
+
+   Copyright (2003) Sandia Corporation.  Under the terms of Contract
+   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
+   certain rights in this software.  This software is distributed under
+   the GNU General Public License.
+
+   See the README file in the top-level LAMMPS directory.
+------------------------------------------------------------------------- */
+
+#ifdef COMPUTE_CLASS
+// clang-format off
+ComputeStyle(pod/atom,ComputePODAtom);
+// clang-format on
+#else
+
+#ifndef LMP_COMPUTE_POD_ATOM_H
+#define LMP_COMPUTE_POD_ATOM_H
+
+#include "compute.h"
+
+namespace LAMMPS_NS {
+
+class ComputePODAtom : public Compute {
+ public:
+  ComputePODAtom(class LAMMPS *, int, char **);
+  ~ComputePODAtom() override;
+  void init() override;
+  void init_list(int, class NeighList *) override;
+  void compute_peratom() override;
+  double memory_usage() override;
+  void lammpsNeighborList(double **x, int **firstneigh, tagint *atomid, int *atomtype,
+                          int *numneigh, double rcutsq, int i);
+  void map_element2type(int narg, char **arg, int nelements);
+
+ private:
+  class NeighList *list;
+  class EAPOD *podptr;
+  double **pod;
+  double cutmax;
+  int nmax;
+  int nij;
+  int nijmax;
+
+  double *tmpmem;    // temporary memory
+  double *rij;       // (xj - xi) for all pairs (I, J)
+  char **elements;
+  int *map;
+  int *ai;    // IDs of atoms I for all pairs (I, J)
+  int *aj;    // IDs of atoms J for all pairs (I, J)
+  int *ti;    // types of atoms I for all pairs (I, J)
+  int *tj;    // types of atoms J  for all pairs (I, J)
+};
+
+}    // namespace LAMMPS_NS
+
+#endif
+#endif

src/ML-POD/compute_pod_global.cpp

@@ -0,0 +1,283 @@
+// clang-format off
+/* ----------------------------------------------------------------------
+   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
+   https://www.lammps.org/, Sandia National Laboratories
+   LAMMPS development team: developers@lammps.org
+
+   Copyright (2003) Sandia Corporation.  Under the terms of Contract
+   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
+   certain rights in this software.  This software is distributed under
+   the GNU General Public License.
+
+   See the README file in the top-level LAMMPS directory.
+------------------------------------------------------------------------- */
+
+#include "compute_pod_global.h"
+
+#include "atom.h"
+#include "comm.h"
+#include "error.h"
+#include "force.h"
+#include "memory.h"
+#include "modify.h"
+#include "neigh_list.h"
+#include "neighbor.h"
+#include "pair.h"
+#include "update.h"
+
+#include <cstring>
+
+#include "eapod.h"
+
+using namespace LAMMPS_NS;
+
+enum { SCALAR, VECTOR, ARRAY };
+
+ComputePODGlobal::ComputePODGlobal(LAMMPS *lmp, int narg, char **arg) :
+    Compute(lmp, narg, arg), list(nullptr), podptr(nullptr), pod(nullptr), tmpmem(nullptr),
+    rij(nullptr), elements(nullptr), map(nullptr), ai(nullptr), aj(nullptr), ti(nullptr),
+    tj(nullptr)
+{
+  array_flag = 1;
+  extarray = 0;
+
+  int nargmin = 6;
+
+  if (narg < nargmin) error->all(FLERR, "Illegal compute {} command", style);
+  if (comm->nprocs > 1) error->all(FLERR, "compute command does not support multi processors");
+
+  std::string pod_file = std::string(arg[3]);      // pod input file
+  std::string coeff_file = std::string(arg[4]);    // coefficient input file
+  podptr = new EAPOD(lmp, pod_file, coeff_file);
+
+  int ntypes = atom->ntypes;
+  memory->create(map, ntypes + 1, "compute_pod_global:map");
+  map_element2type(narg - 5, arg + 5, podptr->nelements);
+
+  size_array_rows = 1 + 3*atom->natoms;
+  size_array_cols = podptr->nCoeffAll;
+  cutmax = podptr->rcut;
+
+  nijmax = 0;
+  pod = nullptr;
+  elements = nullptr;
+}
+
+/* ---------------------------------------------------------------------- */
+
+ComputePODGlobal::~ComputePODGlobal()
+{
+  memory->destroy(map);
+  memory->destroy(pod);
+  delete podptr;
+}
+
+/* ---------------------------------------------------------------------- */
+
+void ComputePODGlobal::init()
+{
+  if (force->pair == nullptr)
+    error->all(FLERR,"Compute pod requires a pair style be defined");
+
+  if (cutmax > force->pair->cutforce)
+    error->all(FLERR,"Compute pod cutoff is longer than pairwise cutoff");
+
+  // need an occasional full neighbor list
+
+  neighbor->add_request(this, NeighConst::REQ_FULL | NeighConst::REQ_OCCASIONAL);
+
+  if (modify->get_compute_by_style("pod").size() > 1 && comm->me == 0)
+    error->warning(FLERR,"More than one compute pod");
+
+ // allocate memory for global array
+  memory->create(pod,size_array_rows,size_array_cols,
+                 "compute_pod_global:pod");
+  array = pod;
+}
+
+/* ---------------------------------------------------------------------- */
+
+void ComputePODGlobal::init_list(int /*id*/, NeighList *ptr)
+{
+  list = ptr;
+}
+
+/* ---------------------------------------------------------------------- */
+
+void ComputePODGlobal::compute_array()
+{
+  // int ntotal = atom->nlocal + atom->nghost;
+  invoked_peratom = update->ntimestep;
+
+  // clear global array
+
+  for (int irow = 0; irow < size_array_rows; irow++)
+    for (int icoeff = 0; icoeff < size_array_cols; icoeff++)
+      pod[irow][icoeff] = 0.0;
+
+  // invoke full neighbor list (will copy or build if necessary)
+
+  neighbor->build_one(list);
+
+  double **x = atom->x;
+  int **firstneigh = list->firstneigh;
+  int *numneigh = list->numneigh;
+  int *type = atom->type;
+  int *ilist = list->ilist;
+  int inum = list->inum;
+  int nClusters = podptr->nClusters;
+  int Mdesc = podptr->Mdesc;
+  int nCoeffPerElement = podptr->nCoeffPerElement;
+
+  double rcutsq = podptr->rcut*podptr->rcut;
+
+  for (int ii = 0; ii < inum; ii++) {
+    int i = ilist[ii];
+    int jnum = numneigh[i];
+
+    // allocate temporary memory
+    if (nijmax < jnum) {
+      nijmax = MAX(nijmax, jnum);
+      podptr->free_temp_memory();
+      podptr->allocate_temp_memory(nijmax);
+    }
+
+    rij = &podptr->tmpmem[0];
+    tmpmem = &podptr->tmpmem[3*nijmax];
+    ai = &podptr->tmpint[0];
+    aj = &podptr->tmpint[nijmax];
+    ti = &podptr->tmpint[2*nijmax];
+    tj = &podptr->tmpint[3*nijmax];
+
+    // get neighbor list for atom i
+    lammpsNeighborList(x, firstneigh, atom->tag, type, numneigh, rcutsq, i);
+
+    if (nij > 0) {
+      // peratom base descriptors
+      double *bd = &podptr->bd[0];
+      double *bdd = &podptr->bdd[0];
+      podptr->peratombase_descriptors(bd, bdd, rij, tmpmem, tj, nij);
+
+      pod[0][nCoeffPerElement*(ti[0]-1)] += 1.0; // one-body descriptor
+
+      if (nClusters>1) {
+        // peratom env descriptors
+        double *pd = &podptr->pd[0];
+        double *pdd = &podptr->pdd[0];
+        podptr->peratomenvironment_descriptors(pd, pdd, bd, bdd, tmpmem, ti[0] - 1,  nij);
+
+        for (int j = 0; j < nClusters; j++) {
+          for (int m=0; m<Mdesc; m++) {
+            int k = nCoeffPerElement*(ti[0]-1) + 1 + m + j*Mdesc; // increment by 1 because of the one-body descriptor
+            pod[0][k] += pd[j]*bd[m];
+            for (int n=0; n<nij; n++) {
+              int ain = 3*ai[n];
+              int ajn = 3*aj[n];
+              int nm = 3*n + 3*nij*m;
+              int nj = 3*n + 3*nij*j;
+              pod[1+ain][k] += bdd[0 + nm]*pd[j] + bd[m]*pdd[0 + nj];
+              pod[2+ain][k] += bdd[1 + nm]*pd[j] + bd[m]*pdd[1 + nj];
+              pod[3+ain][k] += bdd[2 + nm]*pd[j] + bd[m]*pdd[2 + nj];
+              pod[1+ajn][k] -= bdd[0 + nm]*pd[j] + bd[m]*pdd[0 + nj];
+              pod[2+ajn][k] -= bdd[1 + nm]*pd[j] + bd[m]*pdd[1 + nj];
+              pod[3+ajn][k] -= bdd[2 + nm]*pd[j] + bd[m]*pdd[2 + nj];
+            }
+          }
+        }
+      }
+      else {
+        for (int m=0; m<Mdesc; m++) {
+          int k = nCoeffPerElement*(ti[0]-1) + 1 + m; // increment by 1 because of the one-body descriptor
+          pod[0][k] += bd[m];
+          for (int n=0; n<nij; n++) {
+            int ain = 3*ai[n];
+            int ajn = 3*aj[n];
+            int nm = 3*n + 3*nij*m;
+            pod[1+ain][k] += bdd[0 + nm];
+            pod[2+ain][k] += bdd[1 + nm];
+            pod[3+ain][k] += bdd[2 + nm];
+            pod[1+ajn][k] -= bdd[0 + nm];
+            pod[2+ajn][k] -= bdd[1 + nm];
+            pod[3+ajn][k] -= bdd[2 + nm];
+          }
+        }
+      }
+    }
+  }
+}
+
+/* ----------------------------------------------------------------------
+   memory usage
+------------------------------------------------------------------------- */
+
+double ComputePODGlobal::memory_usage()
+{
+  double bytes = 0.0;
+
+  return bytes;
+}
+
+
+void ComputePODGlobal::lammpsNeighborList(double **x, int **firstneigh, tagint *atomid, int *atomtypes,
+                               int *numneigh, double rcutsq, int gi)
+{
+  nij = 0;
+  int itype = map[atomtypes[gi]] + 1;
+  ti[nij] = itype;
+  int m = numneigh[gi];
+  for (int l = 0; l < m; l++) {           // loop over each atom around atom i
+    int gj = firstneigh[gi][l];           // atom j
+    double delx = x[gj][0] - x[gi][0];    // xj - xi
+    double dely = x[gj][1] - x[gi][1];    // xj - xi
+    double delz = x[gj][2] - x[gi][2];    // xj - xi
+    double rsq = delx * delx + dely * dely + delz * delz;
+    if (rsq < rcutsq && rsq > 1e-20) {
+      rij[nij * 3 + 0] = delx;
+      rij[nij * 3 + 1] = dely;
+      rij[nij * 3 + 2] = delz;
+      ai[nij] = atomid[gi]-1;
+      aj[nij] = atomid[gj]-1;
+      ti[nij] = itype;
+      tj[nij] = map[atomtypes[gj]] + 1;
+      nij++;
+    }
+  }
+}
+
+void ComputePODGlobal::map_element2type(int narg, char **arg, int nelements)
+{
+  int i,j;
+  const int ntypes = atom->ntypes;
+
+  // read args that map atom types to elements in potential file
+  // map[i] = which element the Ith atom type is, -1 if "NULL"
+  // nelements = # of unique elements
+  // elements = list of element names
+
+  if (narg != ntypes)
+    error->all(FLERR, "Number of element to type mappings does not match number of atom types");
+
+  if (elements) {
+    for (i = 0; i < nelements; i++) delete[] elements[i];
+    delete[] elements;
+  }
+  elements = new char*[ntypes];
+  for (i = 0; i < ntypes; i++) elements[i] = nullptr;
+
+  nelements = 0;
+  map[0] = -1;
+  for (i = 1; i <= narg; i++) {
+    std::string entry = arg[i-1];
+    if (entry == "NULL") {
+      map[i] = -1;
+      continue;
+    }
+    for (j = 0; j < nelements; j++)
+      if (entry == elements[j]) break;
+    map[i] = j;
+    if (j == nelements) {
+      elements[j] = utils::strdup(entry);
+      nelements++;
+    }
+  }
+}

src/ML-POD/compute_pod_global.h

@@ -0,0 +1,60 @@
+/* -*- c++ -*- ----------------------------------------------------------
+   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
+   https://www.lammps.org/, Sandia National Laboratories
+   LAMMPS development team: developers@lammps.org
+
+   Copyright (2003) Sandia Corporation.  Under the terms of Contract
+   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
+   certain rights in this software.  This software is distributed under
+   the GNU General Public License.
+
+   See the README file in the top-level LAMMPS directory.
+------------------------------------------------------------------------- */
+
+#ifdef COMPUTE_CLASS
+// clang-format off
+ComputeStyle(pod/global,ComputePODGlobal);
+// clang-format on
+#else
+
+#ifndef LMP_COMPUTE_POD_GLOBAL_H
+#define LMP_COMPUTE_POD_GLOBAL_H
+
+#include "compute.h"
+
+namespace LAMMPS_NS {
+
+class ComputePODGlobal : public Compute {
+ public:
+  ComputePODGlobal(class LAMMPS *, int, char **);
+  ~ComputePODGlobal() override;
+  void init() override;
+  void init_list(int, class NeighList *) override;
+  void compute_array() override;
+  double memory_usage() override;
+  void lammpsNeighborList(double **x, int **firstneigh, tagint *atomid, int *atomtype,
+                          int *numneigh, double rcutsq, int i);
+  void map_element2type(int narg, char **arg, int nelements);
+
+ private:
+  class NeighList *list;
+  class EAPOD *podptr;
+  double **pod;
+  double cutmax;
+  int nij;
+  int nijmax;
+
+  double *tmpmem;    // temporary memory
+  double *rij;       // (xj - xi) for all pairs (I, J)
+  char **elements;
+  int *map;
+  int *ai;    // IDs of atoms I for all pairs (I, J)
+  int *aj;    // IDs of atoms J for all pairs (I, J)
+  int *ti;    // types of atoms I for all pairs (I, J)
+  int *tj;    // types of atoms J  for all pairs (I, J)
+};
+
+}    // namespace LAMMPS_NS
+
+#endif
+#endif

src/ML-POD/compute_pod_local.cpp

@@ -0,0 +1,280 @@
+// clang-format off
+/* ----------------------------------------------------------------------
+   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
+   https://www.lammps.org/, Sandia National Laboratories
+   LAMMPS development team: developers@lammps.org
+
+   Copyright (2003) Sandia Corporation.  Under the terms of Contract
+   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
+   certain rights in this software.  This software is distributed under
+   the GNU General Public License.
+
+   See the README file in the top-level LAMMPS directory.
+------------------------------------------------------------------------- */
+
+#include "compute_pod_local.h"
+
+#include "atom.h"
+#include "comm.h"
+#include "error.h"
+#include "force.h"
+#include "memory.h"
+#include "modify.h"
+#include "neigh_list.h"
+#include "neighbor.h"
+#include "pair.h"
+#include "update.h"
+
+#include <cstring>
+
+#include "eapod.h"
+
+using namespace LAMMPS_NS;
+
+enum { SCALAR, VECTOR, ARRAY };
+
+ComputePODLocal::ComputePODLocal(LAMMPS *lmp, int narg, char **arg) :
+    Compute(lmp, narg, arg), list(nullptr), podptr(nullptr), pod(nullptr), tmpmem(nullptr),
+    rij(nullptr), elements(nullptr), map(nullptr), ai(nullptr), aj(nullptr), ti(nullptr),
+    tj(nullptr)
+{
+  array_flag = 1;
+  extarray = 0;
+
+  int nargmin = 6;
+
+  if (narg < nargmin) error->all(FLERR, "Illegal compute {} command", style);
+  if (comm->nprocs > 1) error->all(FLERR, "compute command does not support multi processors");
+
+  std::string pod_file = std::string(arg[3]);      // pod input file
+  std::string coeff_file = std::string(arg[4]);    // coefficient input file
+  podptr = new EAPOD(lmp, pod_file, coeff_file);
+
+  int ntypes = atom->ntypes;
+  memory->create(map, ntypes + 1, "compute_pod_local:map");
+
+  map_element2type(narg - 5, arg + 5, podptr->nelements);
+
+  int numdesc = podptr->Mdesc * podptr->nClusters;
+  size_array_rows = 1 + 3*atom->natoms;
+  size_array_cols = atom->natoms*numdesc;
+  cutmax = podptr->rcut;
+
+  nijmax = 0;
+  pod = nullptr;
+  elements = nullptr;
+}
+
+/* ---------------------------------------------------------------------- */
+
+ComputePODLocal::~ComputePODLocal()
+{
+  memory->destroy(map);
+  memory->destroy(pod);
+  delete podptr;
+}
+
+/* ---------------------------------------------------------------------- */
+
+void ComputePODLocal::init()
+{
+  if (force->pair == nullptr)
+    error->all(FLERR,"Compute pod requires a pair style be defined");
+
+  if (cutmax > force->pair->cutforce)
+    error->all(FLERR,"Compute pod cutoff is longer than pairwise cutoff");
+
+  // need an occasional full neighbor list
+
+  neighbor->add_request(this, NeighConst::REQ_FULL | NeighConst::REQ_OCCASIONAL);
+
+  if (modify->get_compute_by_style("pod").size() > 1 && comm->me == 0)
+    error->warning(FLERR,"More than one compute pod");
+
+ // allocate memory for global array
+  memory->create(pod,size_array_rows,size_array_cols,
+                 "compute_pod_local:pod");
+  array = pod;
+}
+
+/* ---------------------------------------------------------------------- */
+
+void ComputePODLocal::init_list(int /*id*/, NeighList *ptr)
+{
+  list = ptr;
+}
+
+/* ---------------------------------------------------------------------- */
+
+void ComputePODLocal::compute_array()
+{
+  // int ntotal = atom->nlocal + atom->nghost;
+  invoked_peratom = update->ntimestep;
+
+  // clear global array
+
+  for (int irow = 0; irow < size_array_rows; irow++)
+    for (int icoeff = 0; icoeff < size_array_cols; icoeff++)
+      pod[irow][icoeff] = 0.0;
+
+  // invoke full neighbor list (will copy or build if necessary)
+
+  neighbor->build_one(list);
+
+  double **x = atom->x;
+  int **firstneigh = list->firstneigh;
+  int *numneigh = list->numneigh;
+  int *type = atom->type;
+  int *ilist = list->ilist;
+  int inum = list->inum;
+  int nClusters = podptr->nClusters;
+  int Mdesc = podptr->Mdesc;
+
+  double rcutsq = podptr->rcut*podptr->rcut;
+
+  for (int ii = 0; ii < inum; ii++) {
+    int i = ilist[ii];
+    int jnum = numneigh[i];
+
+    // allocate temporary memory
+    if (nijmax < jnum) {
+      nijmax = MAX(nijmax, jnum);
+      podptr->free_temp_memory();
+      podptr->allocate_temp_memory(nijmax);
+    }
+
+    rij = &podptr->tmpmem[0];
+    tmpmem = &podptr->tmpmem[3*nijmax];
+    ai = &podptr->tmpint[0];
+    aj = &podptr->tmpint[nijmax];
+    ti = &podptr->tmpint[2*nijmax];
+    tj = &podptr->tmpint[3*nijmax];
+
+    // get neighbor list for atom i
+    lammpsNeighborList(x, firstneigh, atom->tag, type, numneigh, rcutsq, i);
+
+    if (nij > 0) {
+      // peratom base descriptors
+      double *bd = &podptr->bd[0];
+      double *bdd = &podptr->bdd[0];
+      podptr->peratombase_descriptors(bd, bdd, rij, tmpmem, tj, nij);
+
+      if (nClusters>1) {
+        // peratom env descriptors
+        double *pd = &podptr->pd[0];
+        double *pdd = &podptr->pdd[0];
+        podptr->peratomenvironment_descriptors(pd, pdd, bd, bdd, tmpmem, ti[0] - 1,  nij);
+        for (int k = 0; k < nClusters; k++)
+          for (int m = 0; m < Mdesc; m++) {
+            int imk = m + Mdesc*k +  Mdesc*nClusters*i;
+            pod[0][imk] = pd[k]*bd[m];
+            for (int n=0; n<nij; n++) {
+              int ain = 3*ai[n];
+              int ajn = 3*aj[n];
+              int nm = 3*n + 3*nij*m;
+              int nk = 3*n + 3*nij*k;
+              pod[1 + ain][imk] += bdd[0 + nm]*pd[k] + bd[m]*pdd[0+nk];
+              pod[2 + ain][imk] += bdd[1 + nm]*pd[k] + bd[m]*pdd[1+nk];
+              pod[3 + ain][imk] += bdd[2 + nm]*pd[k] + bd[m]*pdd[2+nk];
+              pod[1 + ajn][imk] -= bdd[0 + nm]*pd[k] + bd[m]*pdd[0+nk];
+              pod[2 + ajn][imk] -= bdd[1 + nm]*pd[k] + bd[m]*pdd[1+nk];
+              pod[3 + ajn][imk] -= bdd[2 + nm]*pd[k] + bd[m]*pdd[2+nk];
+            }
+          }
+      }
+      else {
+        for (int m = 0; m < Mdesc; m++) {
+         int im = m + Mdesc*i;
+         pod[0][im] = bd[m];
+         for (int n=0; n<nij; n++) {
+            int ain = 3*ai[n];
+            int ajn = 3*aj[n];
+            int nm = 3*n + 3*nij*m;
+            pod[1 + ain][im] += bdd[0 + nm];
+            pod[2 + ain][im] += bdd[1 + nm];
+            pod[3 + ain][im] += bdd[2 + nm];
+            pod[1 + ajn][im] -= bdd[0 + nm];
+            pod[2 + ajn][im] -= bdd[1 + nm];
+            pod[3 + ajn][im] -= bdd[2 + nm];
+          }
+        }
+      }
+    }
+  }
+}
+
+/* ----------------------------------------------------------------------
+   memory usage
+------------------------------------------------------------------------- */
+
+double ComputePODLocal::memory_usage()
+{
+  double bytes = 0.0;
+
+  return bytes;
+}
+
+
+void ComputePODLocal::lammpsNeighborList(double **x, int **firstneigh, tagint *atomid, int *atomtypes,
+                               int *numneigh, double rcutsq, int gi)
+{
+  nij = 0;
+  int itype = map[atomtypes[gi]] + 1;
+  ti[nij] = itype;
+  int m = numneigh[gi];
+  for (int l = 0; l < m; l++) {           // loop over each atom around atom i
+    int gj = firstneigh[gi][l];           // atom j
+    double delx = x[gj][0] - x[gi][0];    // xj - xi
+    double dely = x[gj][1] - x[gi][1];    // xj - xi
+    double delz = x[gj][2] - x[gi][2];    // xj - xi
+    double rsq = delx * delx + dely * dely + delz * delz;
+    if (rsq < rcutsq && rsq > 1e-20) {
+      rij[nij * 3 + 0] = delx;
+      rij[nij * 3 + 1] = dely;
+      rij[nij * 3 + 2] = delz;
+      ai[nij] = atomid[gi]-1;
+      aj[nij] = atomid[gj]-1;
+      ti[nij] = itype;
+      tj[nij] = map[atomtypes[gj]] + 1;
+      nij++;
+    }
+  }
+}
+
+void ComputePODLocal::map_element2type(int narg, char **arg, int nelements)
+{
+  int i,j;
+  const int ntypes = atom->ntypes;
+
+  // read args that map atom types to elements in potential file
+  // map[i] = which element the Ith atom type is, -1 if "NULL"
+  // nelements = # of unique elements
+  // elements = list of element names
+
+  if (narg != ntypes)
+    error->all(FLERR, "Number of element to type mappings does not match number of atom types");
+
+  if (elements) {
+    for (i = 0; i < nelements; i++) delete[] elements[i];
+    delete[] elements;
+  }
+  elements = new char*[ntypes];
+  for (i = 0; i < ntypes; i++) elements[i] = nullptr;
+
+  nelements = 0;
+  map[0] = -1;
+  for (i = 1; i <= narg; i++) {
+    std::string entry = arg[i-1];
+    if (entry == "NULL") {
+      map[i] = -1;
+      continue;
+    }
+    for (j = 0; j < nelements; j++)
+      if (entry == elements[j]) break;
+    map[i] = j;
+    if (j == nelements) {
+      elements[j] = utils::strdup(entry);
+      nelements++;
+    }
+  }
+}

src/ML-POD/compute_pod_local.h

@@ -0,0 +1,60 @@
+/* -*- c++ -*- ----------------------------------------------------------
+   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
+   https://www.lammps.org/, Sandia National Laboratories
+   LAMMPS development team: developers@lammps.org
+
+   Copyright (2003) Sandia Corporation.  Under the terms of Contract
+   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
+   certain rights in this software.  This software is distributed under
+   the GNU General Public License.
+
+   See the README file in the top-level LAMMPS directory.
+------------------------------------------------------------------------- */
+
+#ifdef COMPUTE_CLASS
+// clang-format off
+ComputeStyle(pod/local,ComputePODLocal);
+// clang-format on
+#else
+
+#ifndef LMP_COMPUTE_POD_LOCAL_H
+#define LMP_COMPUTE_POD_LOCAL_H
+
+#include "compute.h"
+
+namespace LAMMPS_NS {
+
+class ComputePODLocal : public Compute {
+ public:
+  ComputePODLocal(class LAMMPS *, int, char **);
+  ~ComputePODLocal() override;
+  void init() override;
+  void init_list(int, class NeighList *) override;
+  void compute_array() override;
+  double memory_usage() override;
+  void lammpsNeighborList(double **x, int **firstneigh, tagint *atomid, int *atomtype,
+                          int *numneigh, double rcutsq, int i);
+  void map_element2type(int narg, char **arg, int nelements);
+
+ private:
+  class NeighList *list;
+  class EAPOD *podptr;
+  double **pod;
+  double cutmax;
+  int nij;
+  int nijmax;
+
+  double *tmpmem;    // temporary memory
+  double *rij;       // (xj - xi) for all pairs (I, J)
+  char **elements;
+  int *map;
+  int *ai;    // IDs of atoms I for all pairs (I, J)
+  int *aj;    // IDs of atoms J for all pairs (I, J)
+  int *ti;    // types of atoms I for all pairs (I, J)
+  int *tj;    // types of atoms J  for all pairs (I, J)
+};
+
+}    // namespace LAMMPS_NS
+
+#endif
+#endif

src/ML-POD/compute_podd_atom.cpp

@@ -0,0 +1,282 @@
+// clang-format off
+/* ----------------------------------------------------------------------
+   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
+   https://www.lammps.org/, Sandia National Laboratories
+   LAMMPS development team: developers@lammps.org
+
+   Copyright (2003) Sandia Corporation.  Under the terms of Contract
+   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
+   certain rights in this software.  This software is distributed under
+   the GNU General Public License.
+
+   See the README file in the top-level LAMMPS directory.
+------------------------------------------------------------------------- */
+
+#include "compute_podd_atom.h"
+
+#include "atom.h"
+#include "comm.h"
+#include "error.h"
+#include "force.h"
+#include "memory.h"
+#include "modify.h"
+#include "neigh_list.h"
+#include "neighbor.h"
+#include "pair.h"
+#include "update.h"
+
+#include <cstring>
+
+#include "eapod.h"
+
+using namespace LAMMPS_NS;
+
+enum { SCALAR, VECTOR, ARRAY };
+
+ComputePODDAtom::ComputePODDAtom(LAMMPS *lmp, int narg, char **arg) :
+    Compute(lmp, narg, arg), list(nullptr), podptr(nullptr), pod(nullptr), tmpmem(nullptr),
+    rij(nullptr), elements(nullptr), map(nullptr), ai(nullptr), aj(nullptr), ti(nullptr),
+    tj(nullptr)
+{
+  int nargmin = 6;
+
+  if (narg < nargmin) error->all(FLERR, "Illegal compute {} command", style);
+  if (comm->nprocs > 1) error->all(FLERR, "compute command does not support multi processors");
+
+  std::string pod_file = std::string(arg[3]);      // pod input file
+  std::string coeff_file = std::string(arg[4]);    // coefficient input file
+  podptr = new EAPOD(lmp, pod_file, coeff_file);
+
+  int ntypes = atom->ntypes;
+  memory->create(map, ntypes + 1, "compute_pod_global:map");
+  map_element2type(narg - 5, arg + 5, podptr->nelements);
+
+  cutmax = podptr->rcut;
+
+  nmax = 0;
+  nijmax = 0;
+  pod = nullptr;
+  elements = nullptr;
+
+  if (((((MAXBIGINT*3.0)*atom->natoms)*podptr->nClusters)*podptr->Mdesc) > (MAXSMALLINT*1.0))
+    error->all(FLERR, "Per-atom data too large");
+  size_peratom_cols = 3 * atom->natoms * podptr->Mdesc * podptr->nClusters;
+  peratom_flag = 1;
+}
+
+/* ---------------------------------------------------------------------- */
+
+ComputePODDAtom::~ComputePODDAtom()
+{
+  memory->destroy(map);
+  memory->destroy(pod);
+  delete podptr;
+}
+
+/* ---------------------------------------------------------------------- */
+
+void ComputePODDAtom::init()
+{
+  if (force->pair == nullptr)
+    error->all(FLERR,"Compute pod requires a pair style be defined");
+
+  if (cutmax > force->pair->cutforce)
+    error->all(FLERR,"Compute pod cutoff is longer than pairwise cutoff");
+
+  // need an occasional full neighbor list
+
+  neighbor->add_request(this, NeighConst::REQ_FULL | NeighConst::REQ_OCCASIONAL);
+
+  if (modify->get_compute_by_style("pod").size() > 1 && comm->me == 0)
+    error->warning(FLERR,"More than one compute pod");
+}
+
+
+/* ---------------------------------------------------------------------- */
+
+void ComputePODDAtom::init_list(int /*id*/, NeighList *ptr)
+{
+  list = ptr;
+}
+
+/* ---------------------------------------------------------------------- */
+
+void ComputePODDAtom::compute_peratom()
+{
+  invoked_peratom = update->ntimestep;
+
+  // grow pod array if necessary
+
+  if (atom->natoms > nmax) {
+    memory->destroy(pod);
+    nmax = atom->natoms;
+    if (((((MAXBIGINT*3.0)*atom->natoms)*podptr->nClusters)*podptr->Mdesc) > (MAXSMALLINT*1.0))
+      error->all(FLERR, "Per-atom data too large");
+    int numdesc = 3 * atom->natoms * podptr->Mdesc * podptr->nClusters;
+    memory->create(pod, nmax, numdesc,"podd/atom:pod");
+    array_atom = pod;
+  }
+
+  for (int i = 0; i < atom->natoms; i++)
+    for (int icoeff = 0; icoeff < size_peratom_cols; icoeff++) {
+      pod[i][icoeff] = 0.0;
+    }
+
+  // invoke full neighbor list (will copy or build if necessary)
+
+  neighbor->build_one(list);
+
+  double **x = atom->x;
+  int **firstneigh = list->firstneigh;
+  int *numneigh = list->numneigh;
+  int *type = atom->type;
+  int *ilist = list->ilist;
+  int inum = list->inum;
+  int nClusters = podptr->nClusters;
+  int Mdesc = podptr->Mdesc;
+  double rcutsq = podptr->rcut*podptr->rcut;
+
+  for (int ii = 0; ii < inum; ii++) {
+    int i = ilist[ii];
+    int jnum = numneigh[i];
+
+    // allocate temporary memory
+    if (nijmax < jnum) {
+      nijmax = MAX(nijmax, jnum);
+      podptr->free_temp_memory();
+      podptr->allocate_temp_memory(nijmax);
+    }
+
+    rij = &podptr->tmpmem[0];
+    tmpmem = &podptr->tmpmem[3*nijmax];
+    ai = &podptr->tmpint[0];
+    aj = &podptr->tmpint[nijmax];
+    ti = &podptr->tmpint[2*nijmax];
+    tj = &podptr->tmpint[3*nijmax];
+
+    // get neighbor list for atom i
+    lammpsNeighborList(x, firstneigh, atom->tag, type, numneigh, rcutsq, i);
+
+    if (nij > 0) {
+      // peratom base descriptors
+      double *bd = &podptr->bd[0];
+      double *bdd = &podptr->bdd[0];
+      podptr->peratombase_descriptors(bd, bdd, rij, tmpmem, tj, nij);
+
+      if (nClusters>1) {
+        // peratom env descriptors
+        double *pd = &podptr->pd[0];
+        double *pdd = &podptr->pdd[0];
+        podptr->peratomenvironment_descriptors(pd, pdd, bd, bdd, tmpmem, ti[0] - 1,  nij);
+        for (int n=0; n<nij; n++) {
+          int ain = 3*ai[n];
+          int ajn = 3*aj[n];
+          for (int k = 0; k < nClusters; k++) {
+            for (int m = 0; m < Mdesc; m++) {
+              int mk = m + Mdesc*k;
+              int nm = 3*n + 3*nij*m;
+              int nk = 3*n + 3*nij*k;
+              pod[i][mk + Mdesc*nClusters*0 + Mdesc*nClusters*ain] += bdd[0 + nm]*pd[k] + bd[m]*pdd[0+nk];
+              pod[i][mk + Mdesc*nClusters*1 + Mdesc*nClusters*ain] += bdd[1 + nm]*pd[k] + bd[m]*pdd[1+nk];
+              pod[i][mk + Mdesc*nClusters*2 + Mdesc*nClusters*ain] += bdd[2 + nm]*pd[k] + bd[m]*pdd[2+nk];
+              pod[i][mk + Mdesc*nClusters*0 + Mdesc*nClusters*ajn] -= bdd[0 + nm]*pd[k] + bd[m]*pdd[0+nk];
+              pod[i][mk + Mdesc*nClusters*1 + Mdesc*nClusters*ajn] -= bdd[1 + nm]*pd[k] + bd[m]*pdd[1+nk];
+              pod[i][mk + Mdesc*nClusters*2 + Mdesc*nClusters*ajn] -= bdd[2 + nm]*pd[k] + bd[m]*pdd[2+nk];
+            }
+          }
+        }
+      }
+      else {
+        for (int n=0; n<nij; n++) {
+          int ain = 3*ai[n];
+          int ajn = 3*aj[n];
+          for (int m = 0; m < Mdesc; m++) {
+            int nm = 3*n + 3*nij*m;  // d D_im/ d R_j, m = 1, ..., M, i = 1, ..., N, j = 1, ..., N
+            pod[i][m + Mdesc*0 + Mdesc*ain] += bdd[0 + nm];
+            pod[i][m + Mdesc*1 + Mdesc*ain] += bdd[1 + nm];
+            pod[i][m + Mdesc*2 + Mdesc*ain] += bdd[2 + nm];
+            pod[i][m + Mdesc*0 + Mdesc*ajn] -= bdd[0 + nm];
+            pod[i][m + Mdesc*1 + Mdesc*ajn] -= bdd[1 + nm];
+            pod[i][m + Mdesc*2 + Mdesc*ajn] -= bdd[2 + nm];
+          }
+        }
+      }
+    }
+  }
+}
+
+/* ----------------------------------------------------------------------
+   memory usage
+------------------------------------------------------------------------- */
+
+double ComputePODDAtom::memory_usage()
+{
+  double bytes = 0.0;
+
+  return bytes;
+}
+
+
+void ComputePODDAtom::lammpsNeighborList(double **x, int **firstneigh, tagint *atomid, int *atomtypes,
+                               int *numneigh, double rcutsq, int gi)
+{
+  nij = 0;
+  int itype = map[atomtypes[gi]] + 1;
+  ti[nij] = itype;
+  int m = numneigh[gi];
+  for (int l = 0; l < m; l++) {           // loop over each atom around atom i
+    int gj = firstneigh[gi][l];           // atom j
+    double delx = x[gj][0] - x[gi][0];    // xj - xi
+    double dely = x[gj][1] - x[gi][1];    // xj - xi
+    double delz = x[gj][2] - x[gi][2];    // xj - xi
+    double rsq = delx * delx + dely * dely + delz * delz;
+    if (rsq < rcutsq && rsq > 1e-20) {
+      rij[nij * 3 + 0] = delx;
+      rij[nij * 3 + 1] = dely;
+      rij[nij * 3 + 2] = delz;
+      ai[nij] = atomid[gi]-1;
+      aj[nij] = atomid[gj]-1;
+      ti[nij] = itype;
+      tj[nij] = map[atomtypes[gj]] + 1;
+      nij++;
+    }
+  }
+}
+
+void ComputePODDAtom::map_element2type(int narg, char **arg, int nelements)
+{
+  int i,j;
+  const int ntypes = atom->ntypes;
+
+  // read args that map atom types to elements in potential file
+  // map[i] = which element the Ith atom type is, -1 if "NULL"
+  // nelements = # of unique elements
+  // elements = list of element names
+
+  if (narg != ntypes)
+    error->all(FLERR, "Number of element to type mappings does not match number of atom types");
+
+  if (elements) {
+    for (i = 0; i < nelements; i++) delete[] elements[i];
+    delete[] elements;
+  }
+  elements = new char*[ntypes];
+  for (i = 0; i < ntypes; i++) elements[i] = nullptr;
+
+  nelements = 0;
+  map[0] = -1;
+  for (i = 1; i <= narg; i++) {
+    std::string entry = arg[i-1];
+    if (entry == "NULL") {
+      map[i] = -1;
+      continue;
+    }
+    for (j = 0; j < nelements; j++)
+      if (entry == elements[j]) break;
+    map[i] = j;
+    if (j == nelements) {
+      elements[j] = utils::strdup(entry);
+      nelements++;
+    }
+  }
+}