  Machine learning has recently entered into the mainstream of coarse-grained
(CG) molecular modeling and simulation. While a variety of methods for
incorporating deep learning into these models exist, many of them involve
training neural networks to act directly as the CG force field. This has
several benefits, the most significant of which is accuracy. Neural networks
can inherently incorporate multi-body effects during the calculation of CG
forces, and a well-trained neural network force field outperforms pairwise
basis sets generated from essentially any methodology. However, this comes at a
significant cost. First, these models are typically slower than pairwise force
fields even when accounting for specialized hardware which accelerates the
training and integration of such networks. The second, and the focus of this
paper, is the need for the considerable amount of data needed to train such
force fields. It is common to use 10s of microseconds of molecular dynamics
data to train a single CG model, which approaches the point of eliminating the
CG models usefulness in the first place. As we investigate in this work, this
data-hunger trap from neural networks for predicting molecular energies and
forces can be remediated in part by incorporating equivariant convolutional
operations. We demonstrate that for CG water, networks which incorporate
equivariant convolutional operations can produce functional models using
datasets as small as a single frame of reference data, while networks without
these operations cannot.
