Regularity Priors for the Linear Atomic Cluster Expansion

TL;DR

This paper introduces a regularity prior into linear Atomic Cluster Expansion models to improve the accuracy, stability, and physical realism of machine-learned interatomic potentials, especially in out-of-distribution scenarios.

Contribution

It proposes a novel regularization strategy based on Gaussian broadening within ACE models, demonstrating significant improvements over traditional methods.

Findings

Reduced test errors with prior inclusion

Elimination of spurious minima in potential energy surfaces

Enhanced stability in molecular dynamics simulations

Abstract

Machine-learned interatomic potentials enable large systems to be simulated for long time scales at near ab-initio accuracy. This accuracy is achieved by fitting extremely flexible model architectures to high quality reference data. In practice, this flexibility can cause unwanted behavior such as jagged predicted potential energy surfaces and generally poor out-of-distribution behavior. We investigate a general strategy for incorporating prior beliefs on the regularity of the target energy into linear Atomic Cluster Expansion (ACE) models and explore to what extent this approach improves the quality of the fitted models. Our main focus is an over-regularisation that replicates the Gaussian broadening used in Smooth Overlap of Atomic Positions (SOAP) descriptors within the ACE framework. Numerical tests indicate that the exact form of the prior is non-critical but that including such a prior leads to significant improvement in test errors, consistent repulsion at close-approach, eliminates spurious false minima in the potential energy and enhances stability during molecular dynamics simulations.