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@ -23,49 +23,43 @@ Examples
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Description
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"""""""""""
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Style *rann* computes pairwise interactions for a variety of materials
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using rapid atomistic neural network (RANN) potentials (:ref:`Dickel <Dickel>` , :ref:`Nitol <Nitol>`).
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Neural network potentials work by first generating a series of symmetry functions
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i.e. structural fingerprints from the neighbor list and then using these values
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as the input layer of a neural network. There is a single output neuron in the
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final layer which is the energy. Atomic forces are found by analytical
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derivatives computed via backpropagation. For alloy systems, each element has a unique
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network.
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Pair style *rann* computes pairwise interactions for a variety of
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materials using rapid atomistic neural network (RANN) potentials
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(:ref:`Dickel <Dickel>` , :ref:`Nitol <Nitol>`). Neural network
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potentials work by first generating a series of symmetry functions
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i.e. structural fingerprints from the neighbor list and then using these
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values as the input layer of a neural network. There is a single output
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neuron in the final layer which is the energy. Atomic forces are found
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by analytical derivatives computed via back-propagation. For alloy
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systems, each element has a unique network.
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Potential file syntax
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"""""""""""""""""""""
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The RANN potential is defined by a single text file which contains all the fitting parameters for the alloy system.
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The potential file also defines the active fingerprints, network architecture, activation functions, etc.
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The potential file is divided into several sections which are identified by one of the following keywords:
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The RANN potential is defined by a single text file which contains all
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the fitting parameters for the alloy system. The potential file also
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defines the active fingerprints, network architecture, activation
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functions, etc. The potential file is divided into several sections
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which are identified by one of the following keywords:
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* atomtypes
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* mass
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* fingerprintsperelement
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* fingerprints
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* fingerprintconstants
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* screening (optional)
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* networklayers
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* layersize
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* weight
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* bias
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* activationfunctions
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* calibrationparameters (ignored)
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# is treated as a comment marker, similar to LAMMPS input scripts. Sections are not required to follow a rigid
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ordering, but do require previous definition of prerequisite information. E.g., fingerprintconstants for a
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particular fingerprint must follow the fingerprints definition; layersize for a particular layer must follow
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The '#' character is treated as a comment marker, similar to LAMMPS
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input scripts. Sections are not required to follow a rigid ordering,
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but do require previous definition of prerequisite information. E.g.,
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fingerprintconstants for a particular fingerprint must follow the
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fingerprints definition; layersize for a particular layer must follow
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the declaration of network layers.
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*atomtypes* are defined as follows using element keywords separated by spaces.
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@ -86,15 +80,20 @@ the declaration of network layers.
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mass:Al:
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26.982
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*fingerprintsperelement* specifies how many fingerprints are active for computing the energy of a given atom.
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This number must be specified for each element keyword. Active elements for each fingerprint depend upon the
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type of the central atom and the neighboring atoms. Pairwise fingerprints may be defined for a Mg atom based
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exclusively on its Al neighbors, for example. Bond fingerprints may use two neighborlists of different
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element types. In computing fingerprintsperelement from all defined fingerprints, only the fingerprints
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defined for atoms of a particular element should be considered, regardless of the elements used in its
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neighbor list. In the following code, for example, some fingerprints may compute pairwise fingerprints summing
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contributions about Fe atoms based on a neighbor list of exclusively Al atoms, but if there are no fingerprints
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summing contributions of all neighbors about a central Al atom, then fingerprintsperelement of Al is zero:
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*fingerprintsperelement* specifies how many fingerprints are active for
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computing the energy of a given atom. This number must be specified for
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each element keyword. Active elements for each fingerprint depend upon
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the type of the central atom and the neighboring atoms. Pairwise
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fingerprints may be defined for a Mg atom based exclusively on its Al
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neighbors, for example. Bond fingerprints may use two neighbor lists of
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different element types. In computing fingerprintsperelement from all
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defined fingerprints, only the fingerprints defined for atoms of a
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particular element should be considered, regardless of the elements used
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in its neighbor list. In the following code, for example, some
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fingerprints may compute pairwise fingerprints summing contributions
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about Fe atoms based on a neighbor list of exclusively Al atoms, but if
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there are no fingerprints summing contributions of all neighbors about a
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central Al atom, then fingerprintsperelement of Al is zero:
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.. code-block::
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@ -105,15 +104,21 @@ summing contributions of all neighbors about a central Al atom, then fingerprint
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fingerprintsperelement:Al:
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0
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*fingerprints* specifies the active fingerprints for a certain element combination. Pair fingerprints are
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specified for two elements, while bond fingerprints are specified for three elements. Only one fingerprints
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header should be used for an individual combination of elements. The ordering of the fingerprints in the
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network input layer is determined by the order of element combinations specified by subsequent *fingerprints*
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lines, and the order of the fingerprints defined for each element combination. Multiple fingerprints of the same style or
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different ones may be specified. If the same style and element combination is used for multiple fingerprints,
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they should have different id numbers. The first element specifies the atoms for which this fingerprint is
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computed while the other(s) specify which atoms to use in the neighbor lists for the computation. Switching
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the second and third element type in bond fingerprints has no effect on the computation:
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*fingerprints* specifies the active fingerprints for a certain element
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combination. Pair fingerprints are specified for two elements, while
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bond fingerprints are specified for three elements. Only one
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fingerprints header should be used for an individual combination of
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elements. The ordering of the fingerprints in the network input layer
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is determined by the order of element combinations specified by
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subsequent *fingerprints* lines, and the order of the fingerprints
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defined for each element combination. Multiple fingerprints of the same
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style or different ones may be specified. If the same style and element
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combination is used for multiple fingerprints, they should have
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different id numbers. The first element specifies the atoms for which
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this fingerprint is computed while the other(s) specify which atoms to
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use in the neighbor lists for the computation. Switching the second and
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third element type in bond fingerprints has no effect on the
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computation:
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.. code-block::
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@ -124,25 +129,19 @@ the second and third element type in bond fingerprints has no effect on the comp
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fingerprints:Mg_Al:
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radial_0 radialscreened_0
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The following fingerprint styles are currently defined. See the :ref:`formulation section <fingerprints>` below for their definitions:
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The following fingerprint styles are currently defined. See the
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:ref:`formulation section <fingerprints>` below for their definitions:
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* radial
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* radialscreened
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* radialspin
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* radialscreenedspin
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* bond
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* bondscreened
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* bondspin
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* bondscreenedspin
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*fingerprintconstants* specifies the metaparameters for a defined fingerprint. For all radial styles, re, rc,
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*fingerprintconstants* specifies the meta-parameters for a defined fingerprint. For all radial styles, re, rc,
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alpha, dr, o, and n must be specified. re should usually be the stable interatomic distance, rc is the cutoff
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radius, dr is the cutoff smoothing distance, o is the lowest radial power term (which may be negative), and n
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is the highest power term. The total length of the fingerprint vector is (n-o+1). alpha is a list of decay parameters
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@ -167,12 +166,16 @@ length of the fingerprint vector is m*k.
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fingerprintconstants:Mg_Mg:radialscreened_0:n:
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3
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*screening* specifies the Cmax and Cmin values used in the screening fingerprints. Neighbors' contribution to the
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fingerprint are omitted if they are blocked by a closer neighbor, and reduced if they are partially blocked.
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Larger values of Cmin correspond to neighbors being blocked more easily. Cmax cannot be greater than 3, and
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Cmin cannot be greater than Cmax or less than zero. Screening may be omitted in which case the default values
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Cmax = 2.8, Cmin = 0.8 are used. Since screening is a bond computation, it is specified separately for each
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combination of three elements in which the latter two may be interchanged with no effect.
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*screening* specifies the Cmax and Cmin values used in the screening
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fingerprints. Contributions form neighbors to the fingerprint are
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omitted if they are blocked by a closer neighbor, and reduced if they
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are partially blocked. Larger values of Cmin correspond to neighbors
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being blocked more easily. Cmax cannot be greater than 3, and Cmin
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cannot be greater than Cmax or less than zero. Screening may be omitted
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in which case the default values Cmax = 2.8, Cmin = 0.8 are used. Since
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screening is a bond computation, it is specified separately for each
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combination of three elements in which the latter two may be
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interchanged with no effect.
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.. code-block::
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@ -181,17 +184,18 @@ combination of three elements in which the latter two may be interchanged with n
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screening:Mg_Mg_Mg:Cmin:
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0.400000
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*networklayers* species the size of the neural network for each atom. It counts both the input and output layer
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and so is 2+hiddenlayers.
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*networklayers* species the size of the neural network for each atom.
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It counts both the input and output layer and so is 2 + \<hidden layers\>.
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.. code-block::
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networklayers:Mg:
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3
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*layersize* specifies the length of each layer, including the input layer and output layer. The input layer is
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layer 0. The size of the input layer size must match the summed length of all the fingerprints for that element,
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and the output layer size must be 1:
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*layersize* specifies the length of each layer, including the input
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layer and output layer. The input layer is layer 0. The size of the
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input layer size must match the summed length of all the fingerprints
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for that element, and the output layer size must be 1:
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.. code-block::
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@ -202,8 +206,11 @@ and the output layer size must be 1:
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layersize:Mg:2:
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1
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*weight* specifies the weight for a given element and layer. Weight cannot be specified for the output layer.
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The weight of layer i is a mxn matrix where m is the layer size of i and n is the layer size of i+1:
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*weight* specifies the weight for a given element and layer. Weight
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cannot be specified for the output layer. The weight of layer i is a
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*m* x *n* matrix where *m* is the layer size of *i* and *n* is the layer size of
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*i*\ +1:
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.. code-block::
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@ -212,8 +219,9 @@ The weight of layer i is a mxn matrix where m is the layer size of i and n is th
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w21 w22 w23 ...
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...
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*bias* specifies the bias for a given element and layer. Bias cannot be specified for the output layer.
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The bias of layer i is a nx1 vector where n is the layer size of i+1:
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*bias* specifies the bias for a given element and layer. Bias cannot be
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specified for the output layer. The bias of layer i is a nx1 vector
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where n is the layer size of i+1:
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.. code-block::
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@ -223,8 +231,9 @@ The bias of layer i is a nx1 vector where n is the layer size of i+1:
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b3
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...
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*activationfunctions* specifies the activation function for a given element and layer. Activation functions
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cannot be specified for the output layer:
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*activationfunctions* specifies the activation function for a given
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element and layer. Activation functions cannot be specified for the
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output layer:
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.. code-block::
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@ -233,7 +242,8 @@ cannot be specified for the output layer:
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activationfunctions:Mg:1:
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linear
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The following activation styles are currently specified. See the :ref:`formulation section <activations>` below for their definitions.
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The following activation styles are currently specified. See the
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:ref:`formulation section <activations>` below for their definitions.
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* sigI
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@ -255,19 +265,26 @@ is given by:
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{}^{n+1}\!A_i^{\alpha} = {}^{n}\!F\left({}^{n}\!W_{ij}{\;}^{n}\!A_j^{\alpha}+{}^{n}\!B_i\right)\\\\
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{}^{0}\!A_i^{\alpha} = \left[\begin{array}{c} {}^1\!S\!f^\alpha\\ {}^2\!S\!f^\alpha \\...\\\end{array}\right]
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Here :math:`E^\alpha` is the energy of atom :math:`\alpha`, :math:`{}^n\!F()`, :math:`{}^n\!W_{ij}` and :math:`{}^n\!B_i` are
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the activation function, weight matrix and bias vector of the n-th layer respectively. The
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inputs to the first layer are a collection of structural fingerprints which are collected and reshaped into a single long vector.
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The individual fingerprints may be defined in any order and have various shapes and sizes. Multiple fingerprints of the same
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Here :math:`E^\alpha` is the energy of atom :math:`\alpha`,
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:math:`{}^n\!F()`, :math:`{}^n\!W_{ij}` and :math:`{}^n\!B_i` are the
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activation function, weight matrix and bias vector of the n-th layer
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respectively. The inputs to the first layer are a collection of
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structural fingerprints which are collected and reshaped into a single
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long vector. The individual fingerprints may be defined in any order
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and have various shapes and sizes. Multiple fingerprints of the same
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type and varying parameters may also be defined in the input layer.
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Eight types of structural fingerprints are currently defined. In the following, :math:`\beta` and :math:`\gamma` span the
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full neighborlist of atom :math:`\alpha`. :math:`\delta_i` are decay metaparameters, and :math:`r_e` is a metaparameter
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roughly proportional to the first neighbor distance. :math:`r_c` and :math:`dr` are the neighbor cutoff distance and
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cutoff smoothing distance respectively. :math:`S^{\alpha\beta}` is the MEAM screening function
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:ref:`(Baskes) <Baskes97>`, :math:`s_i^\alpha` and :math:`s_i^\beta` are the atom spin vectors :ref:`(Tranchida) <Tranchida>`.
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:math:`r^{\alpha\beta}` is the distance from atom :math:`\alpha` to atom :math:`\beta`, and :math:`\theta^{\alpha\beta\gamma}`
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is the bond angle:
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Eight types of structural fingerprints are currently defined. In the
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following, :math:`\beta` and :math:`\gamma` span the full neighbor list
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of atom :math:`\alpha`. :math:`\delta_i` are decay meta-parameters, and
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:math:`r_e` is a meta-parameter roughly proportional to the first
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neighbor distance. :math:`r_c` and :math:`dr` are the neighbor cutoff
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distance and cutoff smoothing distance respectively.
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:math:`S^{\alpha\beta}` is the MEAM screening function :ref:`(Baskes)
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<Baskes97>`, :math:`s_i^\alpha` and :math:`s_i^\beta` are the atom spin
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vectors :ref:`(Tranchida) <Tranchida7>`. :math:`r^{\alpha\beta}` is the
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distance from atom :math:`\alpha` to atom :math:`\beta`, and
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:math:`\theta^{\alpha\beta\gamma}` is the bond angle:
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.. math ::
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@ -361,7 +378,7 @@ The activation functions are computed as follows:
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Restrictions
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""""""""""""
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pair_style rann requires the USER-RANN package. It is only enabled if LAMMPS was built with that
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Pair style *rann* is part of the USER-RANN package. It is only enabled if LAMMPS was built with that
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package. Additionally, if any spin fingerprint styles are used LAMMPS must be built with the SPIN
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package as well.
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@ -372,22 +389,24 @@ Cmin = 0.8, Cmax = 2.8.
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----------
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.. _Baskes97:
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.. _Nitol:
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.. _Dickel:
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.. _Dickel1:
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**(Baskes)** Baskes,
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Materials Chemistry and Physics, 50(2), 152-158, (1997).
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.. _Dickel:
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**(Dickel)** Dickel, Francis, and Barrett,
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Computational Materials Science 171 (2020): 109157.
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.. _Nitol:
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**(Nitol)** Nitol, Dickel, and Barrett,
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Computational Materials Science 188 (2021): 110207.
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.. _Tranchida7:
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**(Tranchida)** Tranchida, Plimpton, Thibaudeau and Thompson,
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Journal of Computational Physics, 372, 406-425, (2018).
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Axel Kohlmeyer