Node-equivariant message passing for efficient and accurate machine learning interatomic potentials

Machine learned interatomic potentials, particularly equivariant message-passing (MP) models, have demonstrated high fidelity in representing first-principles data, revolutionizing computational studies in materials science, biophysics, and catalysis. However, these equivariant MP models still incur substantial computational and memory needs due to their expensive tensor product operations over edge space, significantly limiting their applicability in large-scale or long-time simulations. In this work, we propose a novel node-equivariant MP (NEMP) framework that performs equivariant operations between the central node and a virtual summed node encoding structure information of its neighbors. Crucially, NEMP maintains comparable or even superior accuracy across diverse test systems-including molecules, extended systems, and universal potential benchmarks-while achieving 1-2 orders of magnitude reduction in memory and computational costs compared to edge equivariant MP models. In fact, NEMP reaches computational efficiency comparable to that of local descriptor-based models, and enabling previously inaccessible large-scale simulations.