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

2022/05/13 by Ilyes Batatia, Batatia, Ilyes, Simon Batzner +15 · 57 citations
Materials Science · Physics and Astronomy · #Advanced Chemical Physics Studies #Chemical Physics (physics.chem-ph) #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning in Materials Science #Materials Science (cond-mat.mtrl-sci) #X-ray Diffraction in Crystallography

paper · pdf · doi:10.48550/arxiv.2205.06643

openalex publication_date 2022/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The rapid progress of machine learning interatomic potentials over the past couple of years produced 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. In this work, we construct a mathematical framework that unifies these models: ACE is generalised so that it can be recast as one layer of a multi-layer architecture. From another point of view, 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 the unified design space. We demonstrate this by an 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, and shed some light on which design choices are critical for achieving high accuracy. Finally, we present BOTNet (Body-Ordered-Tensor-Network), a much-simplified version of NequIP, which has an interpretable architecture and maintains accuracy on benchmark datasets.

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