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The paper introduces EquiEwald, a novel SO(3)-equivariant neural interatomic potential that incorporates an Ewald-inspired reciprocal-space formulation to model long-range electrostatic and polarization interactions. EquiEwald performs equivariant message passing in reciprocal space using learned equivariant k-space filters and an equivariant inverse transform, enabling the capture of anisotropic, tensorial long-range correlations while maintaining energy-force consistency. Benchmarks on periodic and aperiodic systems demonstrate that EquiEwald achieves improved accuracy, data efficiency, and long-range extrapolation compared to existing methods, establishing it as a promising approach for long-range-capable machine-learning interatomic potentials.
Finally, a neural interatomic potential that accurately models long-range electrostatic interactions without sacrificing SO(3) equivariance or energy-force consistency.
Long-range electrostatic and polarization interactions play a central role in molecular and condensed-phase systems, yet remain fundamentally incompatible with locality-based machine-learning interatomic potentials. Although modern SO(3)-equivariant neural potentials achieve high accuracy for short-range chemistry, they cannot represent the anisotropic, slowly decaying multipolar correlations governing realistic materials, while existing long-range extensions either break SO(3) equivariance or fail to maintain energy-force consistency. Here we introduce EquiEwald, a unified neural interatomic potential that embeds an Ewald-inspired reciprocal-space formulation within an irreducible SO(3)-equivariant framework. By performing equivariant message passing in reciprocal space through learned equivariant k-space filters and an equivariant inverse transform, EquiEwald captures anisotropic, tensorial long-range correlations without sacrificing physical consistency. Across periodic and aperiodic benchmarks, EquiEwald captures long-range electrostatic behavior consistent with ab initio reference data and consistently improves energy and force accuracy, data efficiency, and long-range extrapolation. These results establish EquiEwald as a physically principled paradigm for long-range-capable machine-learning interatomic potentials.
