Rann Hindi Movie Hd Download
Teodosio Shepperd
Pair style rann computes pairwise interactions for a variety ofmaterials using rapid atomistic neural network (RANN) potentials(Dickel , Nitol). Neural networkpotentials work by first generating a series of symmetry functionsi.e. structural fingerprints from the neighbor list and then using thesevalues as the input layer of a neural network. There is a single outputneuron in the final layer which is the energy. Atomic forces are foundby analytical derivatives computed via back-propagation. For alloysystems, each element has a unique network.
The RANN potential is defined by a single text file which contains allthe fitting parameters for the alloy system. The potential file alsodefines the active fingerprints, network architecture, activationfunctions, etc. The potential file is divided into several sectionswhich are identified by one of the following keywords:
fingerprintsperelement specifies how many fingerprints are active forcomputing the energy of a given atom. This number must be specified foreach element keyword. Active elements for each fingerprint depend uponthe type of the central atom and the neighboring atoms. Pairwisefingerprints may be defined for a Mg atom based exclusively on its Alneighbors, for example. Bond fingerprints may use two neighbor lists ofdifferent element types. In computing fingerprintsperelement from alldefined fingerprints, only the fingerprints defined for atoms of aparticular element should be considered, regardless of the elements usedin its neighbor list. In the following code, for example, somefingerprints may compute pairwise fingerprints summing contributionsabout Fe atoms based on a neighbor list of exclusively Al atoms, but ifthere are no fingerprints summing contributions of all neighbors about acentral Al atom, then fingerprintsperelement of Al is zero:
fingerprints specifies the active fingerprints for a certain elementcombination. Pair fingerprints are specified for two elements, whilebond fingerprints are specified for three elements. Only onefingerprints header should be used for an individual combination ofelements. The ordering of the fingerprints in the network input layeris determined by the order of element combinations specified bysubsequent fingerprints lines, and the order of the fingerprintsdefined for each element combination. Multiple fingerprints of the samestyle or different ones may be specified. If the same style and elementcombination is used for multiple fingerprints, they should havedifferent id numbers. The first element specifies the atoms for whichthis fingerprint is computed while the other(s) specify which atoms touse in the neighbor lists for the computation. Switching the second andthird element type in bond fingerprints has no effect on thecomputation:
fingerprintconstants specifies the meta-parameters for a defined fingerprint. For all radial styles, re, rc,alpha, dr, o, and n must be specified. re should usually be the stable interatomic distance, rc is the cutoffradius, dr is the cutoff smoothing distance, o is the lowest radial power term (which may be negative), and nis the highest power term. The total length of the fingerprint vector is (n-o+1). alpha is a list of decay parametersused for exponential decay of radial contributions. It may be set proportionally to the bulk modulus similarlyto MEAM potentials, but other values may provided better fitting in special cases. Bond style fingerprints requirespecification of re, rc, alphak, dr, k, and m. Here m is the power of the bond cosines and k is the number ofdecay parameters. Cosine powers go from 0 to m-1 and are each computed for all values of alphak. Thus the totallength of the fingerprint vector is m*k.
screening specifies the Cmax and Cmin values used in the screeningfingerprints. Contributions form neighbors to the fingerprint areomitted if they are blocked by a closer neighbor, and reduced if theyare partially blocked. Larger values of Cmin correspond to neighborsbeing blocked more easily. Cmax cannot be greater than 3, and Cmincannot be greater than Cmax or less than zero. Screening may be omittedin which case the default values Cmax = 2.8, Cmin = 0.8 are used. Sincescreening is a bond computation, it is specified separately for eachcombination of three elements in which the latter two may beinterchanged with no effect.
layersize specifies the length of each layer, including the inputlayer and output layer. The input layer is layer 0. The size of theinput layer size must match the summed length of all the fingerprintsfor that element, and the output layer size must be 1:
weight specifies the weight for a given element and layer. Weightcannot be specified for the output layer. The weight of layer i is am x n matrix where m is the layer size of i and n is the layer size ofi+1:
Here \(E^\alpha\) is the energy of atom \(\alpha\),\(^n\!F()\), \(^n\!W_ij\) and \(^n\!B_i\) are theactivation function, weight matrix and bias vector of the n-th layerrespectively. The inputs to the first layer are a collection ofstructural fingerprints which are collected and reshaped into a singlelong vector. The individual fingerprints may be defined in any orderand have various shapes and sizes. Multiple fingerprints of the sametype and varying parameters may also be defined in the input layer.
Eight types of structural fingerprints are currently defined. In thefollowing, \(\beta\) and \(\gamma\) span the full neighbor listof atom \(\alpha\). \(\delta_i\) are decay meta-parameters, and\(r_e\) is a meta-parameter roughly proportional to the firstneighbor distance. \(r_c\) and \(dr\) are the neighbor cutoffdistance and cutoff smoothing distance respectively.\(S^\alpha\beta\) is the MEAM screening function (Baskes), \(s_i^\alpha\) and \(s_i^\beta\) are the atom spinvectors (Tranchida). \(r^\alpha\beta\) is thedistance from atom \(\alpha\) to atom \(\beta\), and\(\theta^\alpha\beta\gamma\) is the bond angle:
Pair style rann is part of the ML-RANN package. It is only enabled if LAMMPS was built with thatpackage. Additionally, if any spin fingerprint styles are used LAMMPS must be built with the SPINpackage as well.
An implementation of a rapid artificial neural network (RANN) style potential in the LAMMPS molecular dynamics package is presented here which utilizes angular screening to reduce computational complexity without reducing accuracy. For the smallest neural network architectures, this formalism rivals the modified embedded atom method (MEAM) for speed and accuracy, while the networks approximately one third as fast as MEAM were capable of reproducing the training database with chemical accuracy. The numerical accuracy of the LAMMPS implementation is assessed by verifying conservation of energy and agreement between calculated forces and pressures and the observed derivatives of the energy as well as by assessing the stability of the potential in dynamic simulation. The potential style is tested using a force field for magnesium and the computational efficiency for a variety of architectures is compared to a traditional potential models as well as alternative ANN formalisms. The predictive accuracy is found to rival that of slower methods. While machine learning approaches have been successfully used to represent interatomic potentials, their speed has typically lagged behind conventional formalisms. This is often due to the complexity of the structural fingerprints used to describe the local atomic environment and the large cutoff radii and neighbor lists used in the calculation of these fingerprints. Even recent machine learned methods are at least 10 times slower than traditional formalisms. An implementation of a rapid artificial neural network (RANN) style potential in the LAMMPS molecular dynamics package is presented here which utilizes angular screening to reduce computational complexity without reducing accuracy. For the smallest neural network architectures, this formalism rivals the modified embedded atom method (MEAM) for speed and accuracy, while the networks approximately one third as fast as MEAM were capable of reproducing the training database with chemical accuracy. The numerical accuracy of the LAMMPS implementation is assessed by verifying conservation of energy and agreement between calculated forces and pressures and the observed derivatives of the energy as well as by assessing the stability of the potential in dynamic simulation.
The energy of a particular atom , determined by its environment, is the last of N layers of the neural network. The values for any particular layer, ,after the first is determined by the previous layer and the weight and bias matrices and :
Where is the number of neurons in layer and is a nonlinear activation function. The input layer, is given by the structural fingerprint of the local atomic environment. The ouput layer, , will always contain a single node, representing the energy, and so will always be a row vector and always a single number.
For the RANN style, we use the fingerprint style is motivated by the Modified Embedded Atom Method (MEAM) formalism with the addition of angular screening. In this style, two different kind of input fingerprints are considered. First, simple pair interactions are considered and summed over all the neighbors of a given atom. For a given atom labeled , we define a set of pair potentials interactions with the form:
Where labels all the neighbors atoms of within a cutoff radius , is an integer, different for each member of the pairwise contributions to the fingerprint, is the equilibrium nearest neighbor distance, is an angular screening term, and are metaparameters, which can be tuned to better optimize the potential. The second kind of fingerprint function considers three body terms, with a form similar to the partial electron densities used in MEAM:
A particular ANN potential will consist of a fixed structural fingerprint, number and length of each hidden layer, weight and bias matrices for each layer and activation functions for each layer. For the potentials considered here we have used the following activation functions:
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