Incorporating long-range physics in atomic-scale machine learning

In recent years, atomistic machine learning models have become increasingly popular as a way to perform fast predictions of molecular and material properties with the accuracy of first-principle quantum mechanical calculations,11. The success of these methods has gone hand-in-hand with the progress in constructing representations for molecular and materials configurations that are flexible enough to be transferred across a wide spectrum of different atomic arrangements, while satisfying, at the same time, stringent symmetry constraints.2–62. At the core of the vast majority of transferable machine-learning models for physical properties lies the local nature of the underlying atomistic representation. This is usually constructed by considering the set of atomic coordinates that are included within spherical environments of a given radial cutoff around any arbitrary atomic center.7–97. The prediction of a given physical property is, therefore, formally decomposed in the sum of atom-centered contributions that effectively incorporate information associated with many-body structural correlations between atoms in each local environment.