Self-consistent determination of long-range electrostatics in neural network potentials

Machine learning has the potential to revolutionize the field of molecular simulation through the development of efficient and accurate models of interatomic interactions. Neural networks can model interactions with the accuracy of quantum mechanics-based calculations, but with a fraction of the cost, enabling simulations of large systems over long timescales. However, implicit in the construction of neural network potentials is an assumption of locality, wherein atomic arrangements on the nanometer-scale are used to learn interatomic interactions. Because of this assumption, the resulting neural network models cannot describe long-range interactions that play critical roles in dielectric screening and chemical reactivity. Here, we address this issue by introducing the self-consistent field neural network — a general approach for learning the long-range response of molecular systems in neural network potentials that relies on a physically meaningful separation of the interatomic interactions — and demonstrate its utility by modeling liquid water with and without applied fields.