Electrochemical reactions under constant potential underpin critical processes in energy storage, catalysis, and corrosion but remain challenging to model owing to the voltage insensitivity of conventional machine learning potentials. The lack of a unified framework incorporating grand-canonical constraints into machine-learned models fundamentally limits accurate, scalable simulations of potential-dependent interfacial phenomena. Here, we present a constant-potential, E(3)-equivariant message-passing neural network (CPMPNN) that integrates grand-canonical electronic structure principles with a global excess-charge parameter that is dynamically redistributed via a multihead attention mechanism. The atomic geometry is encoded through a graph neural network that preserves the full symmetry of the Euclidean group in three dimensions (E(3))─including translations, rotations, and reflections. Benchmarking against the grand-canonical DFT confirms that the CPMPNN retains first-principles accuracy while achieving a three-orders-of-magnitude computational speedup. Applied to key electrocatalytic processes─CO dimerization in CO2 reduction and the Volmer step in hydrogen evolution on Cu(100)─CPMPNN captures how the applied potential modulates the reaction thermodynamics, charge distribution, and transition-state structures, providing mechanistic insight into potential-dependent kinetics. By bridging first-principle accuracy with molecular dynamics scalability, CPMPNN provides a transferable framework for operando modeling of electrified interfaces, enabling new mechanistic insights into potential-controlled electrocatalysis.
Chen et al. (Wed,) studied this question.