Research ArticleAPPLIED MATHEMATICS

Machine learning of accurate energy-conserving molecular force fields

+ See all authors and affiliations

Science Advances  05 May 2017:
Vol. 3, no. 5, e1603015
DOI: 10.1126/sciadv.1603015

You are currently viewing the abstract.

View Full Text

Abstract

Using conservation of energy—a fundamental property of closed classical and quantum mechanical systems—we develop an efficient gradient-domain machine learning (GDML) approach to construct accurate molecular force fields using a restricted number of samples from ab initio molecular dynamics (AIMD) trajectories. The GDML implementation is able to reproduce global potential energy surfaces of intermediate-sized molecules with an accuracy of 0.3 kcal mol−1 for energies and 1 kcal mol−1 Å̊−1 for atomic forces using only 1000 conformational geometries for training. We demonstrate this accuracy for AIMD trajectories of molecules, including benzene, toluene, naphthalene, ethanol, uracil, and aspirin. The challenge of constructing conservative force fields is accomplished in our work by learning in a Hilbert space of vector-valued functions that obey the law of energy conservation. The GDML approach enables quantitative molecular dynamics simulations for molecules at a fraction of cost of explicit AIMD calculations, thereby allowing the construction of efficient force fields with the accuracy and transferability of high-level ab initio methods.

Keywords
  • force field
  • machine learning
  • gradient field
  • potential-energy surface
  • energy conservation
  • kernel regression
  • path integrals
  • molecular dynamics

This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license, which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited.

View Full Text