Generalizability of functional forms for interatomic potential models discovered by symbolic regression

Abstract

In recent years, great progress has been made in the use of machine-learning algorithms to develop interatomic potential models. Machine-learned potential models are typically orders of magnitude faster than density functional theory but also orders of magnitude slower than physics-derived models such as the embedded atom method (EAM). In our previous work, we used symbolic regression to develop fast, accurate, and transferrable interatomic potential models for copper with functional forms that resemble those of the EAM. To determine the extent to which the success of these forms was specific to copper, here, we explore the generalizability of these models to other face-centered cubic transition metals and analyze their out-of-sample performance on several material properties. We found that these forms work particularly well on elements that are chemically similar to copper. When compared with optimized Sutton-Chen models, which have similar complexity, the functional forms discovered using symbolic regression perform better across all elements considered, except gold, where they have a similar performance. They perform similarly to a moderately more complex embedded atom form on properties on which they were trained, and they are more accurate on average on other properties. We attribute this improved generalized accuracy to the relative simplicity of the models discovered using symbolic regression. The genetic programming models are found to outperform other models from the literature $\ensuremath{\sim}50%$ of the time in a variety of property predictions, with $\ensuremath{\sim}\frac{1}{10}\mathrm{th}$ the model complexity on average. We discuss the implications of these results to the broader application of symbolic regression to the development of potentials and highlight how models discovered for one element can be used to seed searches for different elements.