  Machine learning (ML) enables the development of interatomic potentials that
promise the accuracy of first principles methods while retaining the low cost
and parallel efficiency of empirical potentials. While ML potentials
traditionally use atom-centered descriptors as inputs, different models such as
linear regression and neural networks can map these descriptors to atomic
energies and forces. This begs the question: what is the improvement in
accuracy due to model complexity irrespective of choice of descriptors? We
curate three datasets to investigate this question in terms of ab initio energy
and force errors: (1) solid and liquid silicon, (2) gallium nitride, and (3)
the superionic conductor LGPS. We further investigate how these errors affect
simulated properties with these models and verify if the improvement in fitting
errors corresponds to measurable improvement in property prediction. Since
linear and nonlinear regression models have different advantages and
disadvantages, the results presented herein help researchers choose models for
their particular application. By assessing different models, we observe
correlations between fitting quantity (e.g. atomic force) error and simulated
property error with respect to ab initio values. Such observations can be
repeated by other researchers to determine the level of accuracy, and hence
model complexity, needed for their particular systems of interest.
