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

2026-03-18

AI Summary

This work proposes EquiEwald, a novel approach that integrates the Ewald summation framework into reciprocal space to address the limitations of existing locality-based machine learning interatomic potentials, which struggle to accurately capture long-range electrostatic and polarization effects while simultaneously preserving SO(3) equivariance and energy–force consistency. By introducing learnable equivariant k-space filters and an equivariant inverse Fourier transform within an irreducible SO(3)-equivariant neural network, EquiEwald enables end-to-end modeling of long-range, anisotropic multipole interactions. The method achieves substantial improvements in prediction accuracy for energies and forces, data efficiency, and long-range extrapolation capability—both for periodic and non-periodic systems—while rigorously maintaining SO(3) equivariance and energy–force consistency, yielding results in close agreement with ab initio reference data.

Technology Category

• Machine Learning: Kernel Methods
• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Multiagent Learning

Application Category

• Economics, Online Markets and Human Computation: Architectures and workflows that use LLMs for crowd work
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• long-range interactions
• SO(3) equivariance
• electrostatics
• machine-learning interatomic potentials
• multipolar correlations

Innovation

• SO(3)-equivariance
• reciprocal space
• long-range interactions
• neural interatomic potential
• Ewald summation