An SO(3)-equivariant reciprocal-space neural potential for long-range interactions

TL;DR

This paper introduces EquiEwald, a novel SO(3)-equivariant neural potential that effectively models long-range electrostatic interactions in materials by embedding an Ewald-inspired reciprocal-space approach, improving accuracy and physical consistency.

Contribution

EquiEwald is the first to integrate an Ewald-inspired reciprocal-space formulation within an SO(3)-equivariant neural network for long-range interactions, maintaining physical principles.

Findings

Captures anisotropic, tensorial long-range correlations.

Improves energy and force prediction accuracy.

Enhances data efficiency and long-range extrapolation.

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.