Optimization methods as applied to parametric identification of interatomic potentials

Abgaryan, K. K.; Posypkin, Mikhail

doi:10.1134/s0965542514120021

Cited by 11 publications

(4 citation statements)

References 5 publications

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“…The optimization of the loss function is an important and rather complex problem. Methods of parametric identification of the Tersoff potential parameters are considered in [26,27]. One of the effective ways is using gradient methods based on automatic differentiation of loss function.…”

Section: Resultsmentioning

confidence: 99%

Multiscale Discrete Element Modeling

2021

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A multiscale approach to discrete element modeling is presented. A distinctive feature of the method is that each macroscopic discrete element has an associated atomic sample representing the material’s atomic structure. The dynamics of the elements on macro and micro levels are described by systems of ordinary differential equations, which are solved in a self-consistent manner. A full cycle of multiscale simulations is applied to polycrystalline silicon. Macroscale elastic properties of silicon were obtained only using data extracted from the quantum mechanical properties. The results of computational experiments correspond well to the reference data.

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Section: Resultsmentioning

confidence: 99%

Multiscale Discrete Element Modeling

2021

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“…where E is total system energy, V ij is the contribution to the interaction energy of atoms with numbers i and j, r ij is the distance between atoms with numbers i and j, f C (r) is a cut-off function, f R (r) and f A (r) are the repulsion and attraction potentials, respectively, and R, D, A, B, n, m, λ 1 , λ 2 , λ 3 , β, γ, c, d and cos(θ 0 ) are potential parameters that are selected in order to reproduce the properties of the simulated material. Methods of parametric identification of the Tersoff potential parameters are considered in papers [26,27]. The initial positions of atoms and their number are determined by the structure of the crystal lattice and the restriction on the minimum size of the simulated space is specified by the structure of the potential.…”

Section: Computation Of An Interval Stress Tensor For Materials With a Covalent Chemical Bondmentioning

confidence: 99%

Sparse Grid Adaptive Interpolation in Problems of Modeling Dynamic Systems with Interval Parameters

2021

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The paper is concerned with the issues of modeling dynamic systems with interval parameters. In previous works, the authors proposed an adaptive interpolation algorithm for solving interval problems; the essence of the algorithm is the dynamic construction of a piecewise polynomial function that interpolates the solution of the problem with a given accuracy. The main problem of applying the algorithm is related to the curse of dimension, i.e., exponential complexity relative to the number of interval uncertainties in parameters. The main objective of this work is to apply the previously proposed adaptive interpolation algorithm to dynamic systems with a large number of interval parameters. In order to reduce the computational complexity of the algorithm, the authors propose using adaptive sparse grids. This article introduces a novelty approach of applying sparse grids to problems with interval uncertainties. The efficiency of the proposed approach has been demonstrated on representative interval problems of nonlinear dynamics and computational materials science.

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“…A plane model of a multilayer piecewise homogeneous material is considered [1], [6] , [4], [2]. The material is represented in the form of a periodic piecewise homogeneous multilayer structure, within the framework of which types of atoms in different layers can differ.…”

Section: Statement Of the Optimization Problemmentioning

confidence: 99%

“…The plane model of a multilayer piecewise homogeneous material considered in the work was proposed in [1], [6] , [4], [2]. In these papers, the problem of unconstrain optimization with box constraints was considered.…”

Section: Introductionmentioning

confidence: 99%

The Application of the Methodology of Fast Automatic Differentiation to Calculate the Gradient of the Potential REBO (LAMMPS)

Amirkhanova¹,

Gorchakov²,

Duysenbaeva³

2019

dtcse

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In this paper, we consider the problem of finding the energy minimum of the aggregate of atoms of a fragment of a planar crystal lattice. To calculate the energy, the Brennor or REBO (reactive empirical bond order) method is used. The REBO potential is calculated using the LAMMPS package (Large-scale Atomic / Molecular Massively Parallel Simulator). As optimization methods, both the gradientless methods and the methods using the first derivatives of the functional are used. To calculate the derivatives, the combined differentiation method, implemented in the LAMMPS package, is used, using sequentially forward and reverse methods of fast automatic differentiation.

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Optimization methods as applied to parametric identification of interatomic potentials

Cited by 11 publications

References 5 publications

Multiscale Discrete Element Modeling

Multiscale Discrete Element Modeling

Sparse Grid Adaptive Interpolation in Problems of Modeling Dynamic Systems with Interval Parameters

The Application of the Methodology of Fast Automatic Differentiation to Calculate the Gradient of the Potential REBO (LAMMPS)

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