Regularity priors for the linear atomic cluster expansion

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 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 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.