The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentials

Abstract

Molecular dynamics simulation is main tool of computational materials science and chemistry, and in the last decade it has been revolutionized by machine learning. The rapid progress of machine learning interatomic potentials produced, just in the last few years, a number of new architectures. Particularly notable among these are the Atomic Cluster Expansion (ACE), which unified many of the earlier ideas around atom density-based descriptors, and Neural Equivariant Interatomic Potentials (NequIP), a message passing neural network with equivariant features that showed state of the art accuracy at the time. In this work, we construct a mathematical framework that unifies these models: ACE is extended and recast as one layer of a multi-layer architecture, while the linearised version of NequIP is understood as a particular sparsification of a much larger polynomial model. Our framework also provides a practical tool for systematically probing different choices in this unified design space. The ablation study of NequIP, via a set of experiments looking at in- and out-of-domain accuracy and smooth extrapolation very far from the training data, sheds some light on which design choices are critical for achieving high accuracy. BOTNet (Body-Ordered- Tensor-Network), a much-simplified version of NequIP has an interpretable architecture and maintains its accuracy on benchmark datasets.