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Title: Learning molecular energies using localized graph kernels

We report that recent machine learning methods make it possible to model potential energy of atomic configurations with chemical-level accuracy (as calculated from ab initio calculations) and at speeds suitable for molecular dynamics simulation. Best performance is achieved when the known physical constraints are encoded in the machine learning models. For example, the atomic energy is invariant under global translations and rotations; it is also invariant to permutations of same-species atoms. Although simple to state, these symmetries are complicated to encode into machine learning algorithms. In this paper, we present a machine learning approach based on graph theory that naturally incorporates translation, rotation, and permutation symmetries. Specifically, we use a random walk graph kernel to measure the similarity of two adjacency matrices, each of which represents a local atomic environment. This Graph Approximated Energy (GRAPE) approach is flexible and admits many possible extensions. Finally, we benchmark a simple version of GRAPE by predicting atomization energies on a standard dataset of organic molecules.
Authors:
 [1] ;  [2] ; ORCiD logo [2]
  1. Universite Paris-Est, CERMICS (ENPC) (France); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Report Number(s):
LA-UR-16-27975
Journal ID: ISSN 0021-9606
Grant/Contract Number:
AC52-06NA25396
Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 146; Journal Issue: 11; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Computer Science; Material Science
OSTI Identifier:
1356139
Alternate Identifier(s):
OSTI ID: 1348278

Ferré, Grégoire, Haut, Terry Scot, and Barros, Kipton Marcos. Learning molecular energies using localized graph kernels. United States: N. p., Web. doi:10.1063/1.4978623.
Ferré, Grégoire, Haut, Terry Scot, & Barros, Kipton Marcos. Learning molecular energies using localized graph kernels. United States. doi:10.1063/1.4978623.
Ferré, Grégoire, Haut, Terry Scot, and Barros, Kipton Marcos. 2017. "Learning molecular energies using localized graph kernels". United States. doi:10.1063/1.4978623. https://www.osti.gov/servlets/purl/1356139.
@article{osti_1356139,
title = {Learning molecular energies using localized graph kernels},
author = {Ferré, Grégoire and Haut, Terry Scot and Barros, Kipton Marcos},
abstractNote = {We report that recent machine learning methods make it possible to model potential energy of atomic configurations with chemical-level accuracy (as calculated from ab initio calculations) and at speeds suitable for molecular dynamics simulation. Best performance is achieved when the known physical constraints are encoded in the machine learning models. For example, the atomic energy is invariant under global translations and rotations; it is also invariant to permutations of same-species atoms. Although simple to state, these symmetries are complicated to encode into machine learning algorithms. In this paper, we present a machine learning approach based on graph theory that naturally incorporates translation, rotation, and permutation symmetries. Specifically, we use a random walk graph kernel to measure the similarity of two adjacency matrices, each of which represents a local atomic environment. This Graph Approximated Energy (GRAPE) approach is flexible and admits many possible extensions. Finally, we benchmark a simple version of GRAPE by predicting atomization energies on a standard dataset of organic molecules.},
doi = {10.1063/1.4978623},
journal = {Journal of Chemical Physics},
number = 11,
volume = 146,
place = {United States},
year = {2017},
month = {3}
}