An SO(3)-equivariant reciprocal-space neural potential for long-range interactions
Abstract
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.
Cite
@article{arxiv.2603.18389,
title = {An SO(3)-equivariant reciprocal-space neural potential for long-range interactions},
author = {Lingfeng Zhang and Taoyong Cui and Dongzhan Zhou and Lei Bai and Sufei Zhang and Luca Rossi and Mao Su and Wanli Ouyang and Pheng-Ann Heng},
journal= {arXiv preprint arXiv:2603.18389},
year = {2026}
}