Incorporating long-range physics in atomic-scale machine learning

TL;DR

This paper introduces a novel machine learning framework that incorporates long-range physical effects, such as electrostatics, into atomic-scale models to improve their accuracy and transferability.

Contribution

It proposes non-local, equivariant feature representations that capture long-range physics, enhancing atomistic machine learning models beyond local approximations.

Findings

Successfully models electrostatic energy of point charges

Accurately predicts binding curves of charged molecular dimers

Represents dielectric response of liquid water effectively

Abstract

The most successful and popular machine learning models of atomic-scale properties derive their transferability from a locality ansatz. The properties of a large molecule or a bulk material are written as a sum over contributions that depend on the configurations within finite atom-centered environments. The obvious downside of this approach is that it cannot capture non-local, non-additive effects such as those arising due to long-range electrostatics or quantum interference. We propose a solution to this problem by introducing non-local representations of the system that are remapped as feature vectors that are defined locally and are equivariant in O(3). We consider in particular one form that has the same asymptotic behavior as the electrostatic potential. We demonstrate that this framework can capture non-local, long-range physics by building a model for the electrostatic energy of randomly distributed point-charges, for the unrelaxed binding curves of charged organic molecular dimers, and for the electronic dielectric response of liquid water. By combining a representation of the system that is sensitive to long-range correlations with the transferability of an atom-centered additive model, this method outperforms current state-of-the-art machine-learning schemes, and provides a conceptual framework to incorporate non-local physics into atomistic machine learning.