Simple and Efficient Equivariant Message-Passing Neural Network Model for Non-local Potential Energy Surfaces

Machine learning potential has become increasingly successful in atomistic simulations. Many of these potentials are based on an atomistic representation in a local environment, but an efficient description of nonlocal interactions that exceed a common local environment remains a challenge. Herein, we propose a simple and efficient equivariant model, EquiREANN, to effectively represent a nonlocal potential energy surface. It relies on a physically inspired message-passing framework, where the fundamental descriptors are linear combinations of atomic orbitals, while both invariant orbital coefficients and the equivariant orbital functions are iteratively updated. We demonstrate that this EquiREANN model is able to describe the subtle potential energy variation due to the nonlocal structural change with high accuracy and little extra computational cost than an invariant message passing model. Our work offers a generalized approach to create equivariant message-passing adaptations of other advanced local many-body descriptors.