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

arXiv: https://arxiv.org/abs/2603.18389 · HTML: https://mlsanity.com/paper/2603.18389/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 49 references that are in the map.
- First posted on arXiv 19 Mar 2026.

## Builds on (most cited first, 19 of 19)

- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [The Open Catalyst 2020 (OC20) Dataset and Community Challenges](https://mlsanity.com/paper/2010.09990/) (2020)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representations](https://mlsanity.com/paper/2306.12059/) (2023)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNs](https://mlsanity.com/paper/2302.03655/) (2023)
- [SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effects](https://mlsanity.com/paper/2105.00304/) (2021)
- [A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems](https://mlsanity.com/paper/2312.07511/) (2023)
- [Spherical Channels for Modeling Atomic Interactions](https://mlsanity.com/paper/2206.14331/) (2022)
- [Ewald-based Long-Range Message Passing for Molecular Graphs](https://mlsanity.com/paper/2303.04791/) (2023)
- [Latent Ewald summation for machine learning of long-range interactions](https://mlsanity.com/paper/2408.15165/) (2024)
- [Physics-inspired Equivariant Descriptors of Non-bonded Interactions](https://mlsanity.com/paper/2308.13208/) (2023)
- [Capturing long-range interaction with reciprocal space neural network](https://mlsanity.com/paper/2211.16684/) (2022)

## Built on by (most cited first, 2 of 2)

- [Atomistic Modeling of Chemical Disorder in Materials: Bridging Conventional Methods and AI-Assisted Approaches](https://mlsanity.com/paper/2605.19124/) (2026)
- [NEMORA: Neural Equivariant Multipole Operators for Long-Range Atomistic Learning](https://mlsanity.com/paper/2610.10776/) (2026)

## 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.