  Machine learning has the potential to revolutionize the field of molecular
simulation through the development of efficient and accurate models of
interatomic interactions. In particular, neural network models can describe
interactions at the level of accuracy of quantum mechanics-based calculations,
but with a fraction of the cost, enabling the simulation of large systems over
long timescales with ab initio accuracy. However, implicit in the construction
of neural network potentials is an assumption of locality, wherein atomic
arrangements on the scale of about a nanometer 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. To address this issue, we introduce the
self-consistent field neural network (SCFNN) model -- a general approach for
learning the long-range response of molecular systems in neural network
potentials. The SCFNN model relies on a physically meaningful separation of the
interatomic interactions into short- and long-range components, with a separate
network to handle each component. We demonstrate the success of the SCFNN
approach in modeling the dielectric properties of bulk liquid water, and show
that the SCFNN model accurately predicts long-range polarization correlations
and the response of water to applied electrostatic fields. Importantly, because
of the separation of interactions inherent in our approach, the SCFNN model can
be combined with many existing approaches for building neural network
potentials. Therefore, we expect the SCFNN model to facilitate the proper
description of long-range interactions in a wide-variety of machine
learning-based force fields.
