# Capturing long-range interaction with reciprocal space neural network

arXiv: https://arxiv.org/abs/2211.16684 · HTML: https://mlsanity.com/paper/2211.16684/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 52 references that are in the map.
- First posted on arXiv 30 Nov 2022.

## Builds on (most cited first, 15 of 15)

- [Strategies for Pre-training Graph Neural Networks](https://mlsanity.com/paper/1905.12265/) (2019)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [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)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [Do Transformers Really Perform Bad for Graph Representation?](https://mlsanity.com/paper/2106.05234/) (2021)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [DScribe: Library of Descriptors for Machine Learning in Materials Science](https://mlsanity.com/paper/1904.08875/) (2019)
- [An invertible crystallographic representation for general inverse design of inorganic crystals with targeted properties](https://mlsanity.com/paper/2005.07609/) (2020)
- [Crystal Twins: Self-supervised Learning for Crystalline Material Property Prediction](https://mlsanity.com/paper/2205.01893/) (2022)
- [Orbital Graph Convolutional Neural Network for Material Property Prediction](https://mlsanity.com/paper/2008.06415/) (2020)
- [Equivariant representations for molecular Hamiltonians and N-center atomic-scale properties](https://mlsanity.com/paper/2109.12083/) (2021)
- [Geometric Transformer for End-to-End Molecule Properties Prediction](https://mlsanity.com/paper/2110.13721/) (2021)
- [Complex Spin Hamiltonian Represented by Artificial Neural Network](https://mlsanity.com/paper/2110.00724/) (2021)

## Built on by (most cited first, 13 of 13)

- [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)
- [Neural P3M: A Long-Range Interaction Modeling Enhancer for Geometric GNNs](https://mlsanity.com/paper/2409.17622/) (2024)
- [A universal augmentation framework for long-range electrostatics in machine learning interatomic potentials](https://mlsanity.com/paper/2507.14302/) (2025)
- [Learning charges and long-range interactions from energies and forces](https://mlsanity.com/paper/2412.15455/) (2024)
- [Learning Non-Local Molecular Interactions via Equivariant Local Representations and Charge Equilibration](https://mlsanity.com/paper/2501.19179/) (2025)
- [Beyond Structure: Invariant Crystal Property Prediction with Pseudo-Particle Ray Diffraction](https://mlsanity.com/paper/2509.21778/) (2025)
- [An SO(3)-equivariant reciprocal-space neural potential for long-range interactions](https://mlsanity.com/paper/2603.18389/) (2026)
- [From Peptides to Nanostructures: A Euclidean Transformer for Fast and Stable Machine Learned Force Fields](https://mlsanity.com/paper/2309.15126/) (2023)
- [ReciNet: Reciprocal Space-Aware Long-Range Modeling for Crystalline Property Prediction](https://mlsanity.com/paper/2502.02748/) (2025)
- [Long-range electrostatics for machine learning interatomic potentials is easier than we thought](https://mlsanity.com/paper/2512.18029/) (2025)
- [Physics-Informed Long-Range Coulomb Correction for Machine-learning Hamiltonians](https://mlsanity.com/paper/2603.20007/) (2026)
- [NEMORA: Neural Equivariant Multipole Operators for Long-Range Atomistic Learning](https://mlsanity.com/paper/2610.10776/) (2026)

## Abstract (arXiv)

Machine Learning (ML) interatomic models and potentials have been widely employed in simulations of materials. Long-range interactions often dominate in some ionic systems whose dynamics behavior is significantly influenced. However, the long-range effect such as Coulomb and Van der Wales potential is not considered in most ML interatomic potentials. To address this issue, we put forward a method that can take long-range effects into account for most ML local interatomic models with the reciprocal space neural network. The structure information in real space is firstly transformed into reciprocal space and then encoded into a reciprocal space potential or a global descriptor with full atomic interactions. The reciprocal space potential and descriptor keep full invariance of Euclidean symmetry and choice of the cell. Benefiting from the reciprocal-space information, ML interatomic models can be extended to describe the long-range potential including not only Coulomb but any other long-range interaction. A model NaCl system considering Coulomb interaction and the GaxNy system with defects are applied to illustrate the advantage of our approach. At the same time, our approach helps to improve the prediction accuracy of some global properties such as the band gap where the full atomic interaction beyond local atomic environments plays a very important role. In summary, our work has expanded the ability of current ML interatomic models and potentials when dealing with the long-range effect, hence paving a new way for accurate prediction of global properties and large-scale dynamic simulations of systems with defects.