NequIP—Equivariance Enables Machine Learning Interatomic Potentials at Unprecedented Sample Efficiency and Accuracy

Representations of materials for the purpose of Machine Learning must obey the physical symmetries of 3D space: translation, rotation, and mirrors, and additionally the permutation with respect to indexing of atoms. In most leading approaches to Machine Learning Interatomic Potentials, these constraints are satisifed by invariant representations that only operate on distances and angles. In this work, we discuss the recently introduced framework of Neural Equivariant Interatomic Potentials (NequIP), a deep learning approach that builds on E(3)-equivariant convolutions over geometric tensors instead of E(3)-invariant convolutions over scalars only. We demonstrate that by leveraging equivariance, the proposed method significantly outperforms all existing Machine Learning Interatomic Potentials. We further show how equivariance greatly improves the sample efficiency of the approach and can outperform existing invariant methods with up to 1,000 times fewer training data. We discuss the application of NequIP to a wide variety of materials systems, including Li diffusion in a superionic conductor, glass formation in a complex lithium phosphate, bulk water, and heterogeneous reactions. Finally, we discuss potential reasons for the high sample efficiency of equivariant interatomic potentials.