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Machine learning representation for atomic forces and energies

We present machine learning models for fast estimating atomic forces and energies. In our method, the total energy of a system is approximated as the summation of atomic energy which is the interaction energy with its surrounding chemical environment within a certain cutoff radius. | VNU Journal of Science Mathematics Physics Vol. 36 No. 2 2020 74-80 Original Article Machine Learning Representation for Atomic Forces and Energies Pham Tien Lam1 2 Nguyen Van Duy1 2 Nguyen Tien Cuong3 1 Phenikaa Institute for Advanced Study Phenikaa University Ha Dong Hanoi Vietnam 2 Faculty of Computer Science Phenikaa University Ha Dong Hanoi Vietnam 3 VNU University of Science 334 Nguyen Trai Thanh Xuan Hanoi Vietnam Received 13 February 2020 Revised 13 March 2020 Accepted 25 March 2020 Abstract We present machine learning models for fast estimating atomic forces and energies. In our method the total energy of a system is approximated as the summation of atomic energy which is the interaction energy with its surrounding chemical environment within a certain cutoff radius. Atomic energy is decomposed into two-body terms which are expressed as a linear combination of basis functions. For the force exerted on an atom we employ a linear combination of a set of basis functions for representing pairwise force. We use least-square linear regression regularized by the l2-norm known as Ridge regression to estimate model parameters. We demonstrate that we can train linear model to accurately predict atomic forces and energies in comparison to density- functional-theory DFT calculations for crystalline and amorphous silicon. The machine learning force model is then applied to calculate the phonon dispersion of crystalline silicon. The result shows reasonable agreement with DFT calculations. Keywords Machine Learning molecular dynamics force field materials informatics. 1. Introduction The computation of the energies especially the forces of a chemical system play a central role in the computational design of matter and materials. The energies and forces can be obtained by performing electronic structure calculations such as those based on density functional theory DFT 1 3 . Although ________ Corresponding author. Email address lam.phamtien@phenikaa-uni.edu.vn https .