Long-range electrostatics in atomistic machine learning: a physical perspective

Abstract

The inclusion of long-range electrostatics in atomistic machine learning (ML) is receiving increasing attention for achieving quantum-mechanical accuracy in predicting a wide range of molecular and material properties. However, there is still no general prescription for how long-range physical effects should be incorporated into a model while preserving the well-established locality principles underlying most transferable ML representations. Here, we provide a physical perspective on this problem by discussing how distinct contributions to a system's electrostatics can be captured through different learning paradigms. Specifically, we distinguish between local charge models, which rely either on explicit charge-density decompositions or implicit auxiliary variables, and models in which a notion of nonlocality is deliberately introduced, either via self-consistent procedures or by using nonlocal descriptors and learning architectures. We further address the related aspect of incorporating finite-field effects through coupling to the system's polarization, relevant for applications involving an external electric bias. We conclude by discussing implications for simulations of electrochemical interfaces, where long-range electrostatics are essential to capture the interplay between charge redistribution, interfacial dynamics, and ionic screening, as well as for ionic transport phenomena, which, although less explored, appear far less sensitive to their inclusion.