Large-scale equivariant deep learning of atomistic force fields

The physics of atomic systems obeys a set of symmetries, namely permutation, rotation, translation, and inversion. The predictions of machine learning models on these systems should likewise respect those symmetries. In particular, many important properties, such as the potential energy, are invariant under these symmetries: unchanged when the system undergoes a symmetry transform. This invariance has traditionally been enforced by using generic machine learning models whose inputs are restricted to already invariant data featurizations such as interatomic distances or angles.

This talk discusses Allegro and NequIP, two methods that are instead equivariant to the Euclidean group E(3) and operate directly on the unprocessed 3D geometry: their inputs, internal latent representations, and predictions can contain not only invariants, but also equivariant geometric vectors and higher-order tensors, which transform correspondingly when the input is transformed. Applied to machine learning interatomic potentials, this approach yields remarkable improvements in accuracy, configurational and chemical generalization, simulation stability, and sample efficiency. I will discuss how equivariance is mathematically enabled, the theoretical properties and motivations of the proposed approach, and finally demonstrate the methods through example applications to complex catalytic and diffusive materials, organic molecules, ionic liquids, and biomolecules.