Equivariant Interatomic Potentials without Tensor Products

Foundational machine-learned interatomic potentials have emerged as powerful tools for atomistic simulations, promising near first-principles accuracy across diverse chemical spaces at a fraction of the cost of quantum-mechanical calculations. However, the most accurate equivariant architectures rely on Clebsch-Gordan tensor products whose computational cost scales steeply with angular resolution, creating a trade-off between model expressiveness and inference speed that ultimately limits practical applications. Here we introduce Geodite, an equivariant message-passing architecture that replaces tensor products while incorporating physical priors to ensure smooth, well-behaved potential energy surfaces. Trained on the Materials Project trajectories dataset of inorganic crystals, Geodite-MP achieves accuracy competitive with leading methods on benchmarks for materials stability prediction, thermal conductivity, phonon-derived properties, and nanosecond-scale molecular dynamics, while running $3\text{--}5\times$ faster than models performing similarly. By combining predictive accuracy, computational efficiency, and physicality, Geodite enables faster large-scale atomistic simulations and high-throughput screening that would otherwise be computationally prohibitive.