  By adopting a perspective informed by contemporary liquid state theory, we
consider how to train an artificial neural network potential to describe
inhomogeneous, disordered systems. We find that neural network potentials based
on local representations of atomic environments are capable of describing some
properties of liquid-vapor interfaces, but typically fail for properties that
depend on unbalanced long-ranged interactions which build up in the presence of
broken translation symmetry. These same interactions cancel in the
translationally invariant bulk, allowing local neural network potentials to
describe bulk properties correctly. By incorporating explicit models of the
slowly-varying long-ranged interactions and training neural networks only on
the short ranged components, we can arrive at potentials that robustly recover
interfacial properties. We find that local neural network models can sometimes
approximate a local molecular field potential to correct for the truncated
interactions, but this behavior is variable and hard to learn. Generally, we
find that models with explicit electrostatics are easier to train and have
higher accuracy. We demonstrate this perspective in a simple model of an
asymmetric dipolar fluid where the exact long-ranged interaction is known, and
in an ab initio water model where it is approximated.
