Machine Learning of Accurate Energy-Conserving Molecular Force Fields

TL;DR

This paper introduces a gradient-domain machine learning method that efficiently constructs accurate, energy-conserving molecular force fields from limited ab initio data, enabling cost-effective molecular dynamics simulations.

Contribution

The work presents a novel GDML approach that learns energy-conserving force fields in a vector-valued function space, achieving high accuracy with minimal training data.

Findings

Reproduces potential energy surfaces with 0.3 kcal/mol energy accuracy

Achieves atomic force accuracy of 1 kcal/mol/Å

Validates on diverse molecules including benzene and aspirin

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 $\text{mol}^{-1}$ for energies and 1 kcal $\text{mol}^{-1}$ $\text{\AA}^{-1}$ 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.