mlsanityData to 7 Oct 2026

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

arXiv 2603.18389 ↗First posted 19 Mar 2026physics.chem-ph cs.AIcited by 1

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Abstract (arXiv)

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.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 19 of its 49 references that are in the map. First posted on arXiv 19 Mar 2026.

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19 of 49 references.

References · 19

  1. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  2. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 701
  3. 2017SchNet: A continuous-filter convolutional neural network for modeling quantum interactionscited by 569
  4. 2020Directional Message Passing for Molecular Graphscited by 556
  5. 2022MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fieldscited by 467
  6. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 348
  7. 2022Learning Local Equivariant Representations for Large-Scale Atomistic Dynamicscited by 254
  8. 2020The Open Catalyst 2020 (OC20) Dataset and Community Challengescited by 246
  9. 2020Machine Learning Force Fieldscited by 204
  10. 2023EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representationscited by 201
  11. 2022e3nn: Euclidean Neural Networkscited by 171
  12. 2023Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNscited by 113
7 more
  1. 2021SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effectscited by 103
  2. 2023A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systemscited by 65
  3. 2022Spherical Channels for Modeling Atomic Interactionscited by 47
  4. 2023Ewald-based Long-Range Message Passing for Molecular Graphscited by 46
  5. 2024Latent Ewald summation for machine learning of long-range interactionscited by 26
  6. 2022Capturing long-range interaction with reciprocal space neural networkcited by 13
  7. 2023Physics-inspired Equivariant Descriptors of Non-bonded Interactionscited by 13

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026NEMORA: Neural Equivariant Multipole Operators for Long-Range Atomistic Learningcited by 0