# Ewald-based Long-Range Message Passing for Molecular Graphs

arXiv: https://arxiv.org/abs/2303.04791 · HTML: https://mlsanity.com/paper/2303.04791/

## Key facts

- Cited by 46 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 58 references that are in the map.
- First posted on arXiv 8 Mar 2023.

## Builds on (most cited first, 26 of 26)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Rethinking Graph Transformers with Spectral Attention](https://mlsanity.com/paper/2106.03893/) (2021)
- [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)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [The Open Catalyst 2020 (OC20) Dataset and Community Challenges](https://mlsanity.com/paper/2010.09990/) (2020)
- [GraphiT: Encoding Graph Structure in Transformers](https://mlsanity.com/paper/2106.05667/) (2021)
- [SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effects](https://mlsanity.com/paper/2105.00304/) (2021)
- [The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentials](https://mlsanity.com/paper/2205.06643/) (2022)
- [Non-Local Graph Neural Networks](https://mlsanity.com/paper/2005.14612/) (2020)
- [On the Universality of Rotation Equivariant Point Cloud Networks](https://mlsanity.com/paper/2010.02449/) (2020)
- [GemNet-OC: Developing Graph Neural Networks for Large and Diverse Molecular Simulation Datasets](https://mlsanity.com/paper/2204.02782/) (2022)
- [Molecular Mechanics-Driven Graph Neural Network with Multiplex Graph for Molecular Structures](https://mlsanity.com/paper/2011.07457/) (2020)
- [So3krates: Equivariant attention for interactions on arbitrary length-scales in molecular systems](https://mlsanity.com/paper/2205.14276/) (2022)
- [Ab-Initio Potential Energy Surfaces by Pairing GNNs with Neural Wave Functions](https://mlsanity.com/paper/2110.05064/) (2021)
- [Capturing long-range interaction with reciprocal space neural network](https://mlsanity.com/paper/2211.16684/) (2022)

## Built on by (most cited first, 30 of 46)

- [Soft Prompt Threats: Attacking Safety Alignment and Unlearning in Open-Source LLMs through the Embedding Space](https://mlsanity.com/paper/2402.09063/) (2024)
- [A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems](https://mlsanity.com/paper/2312.07511/) (2023)
- [Efficient Approximations of Complete Interatomic Potentials for Crystal Property Prediction](https://mlsanity.com/paper/2306.10045/) (2023)
- [Latent Ewald summation for machine learning of long-range interactions](https://mlsanity.com/paper/2408.15165/) (2024)
- [Navigating protein landscapes with a machine-learned transferable coarse-grained model](https://mlsanity.com/paper/2310.18278/) (2023)
- [Spatio-Spectral Graph Neural Networks](https://mlsanity.com/paper/2405.19121/) (2024)
- [Crystalformer: Infinitely Connected Attention for Periodic Structure Encoding](https://mlsanity.com/paper/2403.11686/) (2024)
- [Implicit Transfer Operator Learning: Multiple Time-Resolution Surrogates for Molecular Dynamics](https://mlsanity.com/paper/2305.18046/) (2023)
- [Euclidean Fast Attention -- Machine Learning Global Atomic Representations at Linear Cost](https://mlsanity.com/paper/2412.08541/) (2024)
- [Neural Atoms: Propagating Long-range Interaction in Molecular Graphs through Efficient Communication Channel](https://mlsanity.com/paper/2311.01276/) (2023)
- [Gaussian Plane-Wave Neural Operator for Electron Density Estimation](https://mlsanity.com/paper/2402.04278/) (2024)
- [Neural Pfaffians: Solving Many Many-Electron Schr"odinger Equations](https://mlsanity.com/paper/2405.14762/) (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 Equivariant Non-Local Electron Density Functionals](https://mlsanity.com/paper/2410.07972/) (2024)
- [chemtrain-deploy: A parallel and scalable framework for machine learning potentials in million-atom MD simulations](https://mlsanity.com/paper/2506.04055/) (2025)
- [Learning Interatomic Potentials at Multiple Scales](https://mlsanity.com/paper/2310.13756/) (2023)
- [Learning Non-Local Molecular Interactions via Equivariant Local Representations and Charge Equilibration](https://mlsanity.com/paper/2501.19179/) (2025)
- [DualEquiNet: A Dual-Space Hierarchical Equivariant Network for Large Biomolecules](https://mlsanity.com/paper/2506.19862/) (2025)
- [HollowFlow: Efficient Sample Likelihood Evaluation using Hollow Message Passing](https://mlsanity.com/paper/2510.21542/) (2025)
- [Beyond Structure: Invariant Crystal Property Prediction with Pseudo-Particle Ray Diffraction](https://mlsanity.com/paper/2509.21778/) (2025)
- [Equivariant Matrix Function Neural Networks](https://mlsanity.com/paper/2310.10434/) (2023)
- [On Representing Electronic Wave Functions with Sign Equivariant Neural Networks](https://mlsanity.com/paper/2403.05249/) (2024)
- [SE3Set: Harnessing equivariant hypergraph neural networks for molecular representation learning](https://mlsanity.com/paper/2405.16511/) (2024)
- [Machine-Learning Interatomic Potentials for Long-Range Systems](https://mlsanity.com/paper/2502.04668/) (2025)
- [Generalization of Long-Range Machine Learning Potentials in Complex Chemical Spaces](https://mlsanity.com/paper/2512.10989/) (2025)
- [Global Plane Waves From Local Gaussians: Periodic Charge Densities in a Blink](https://mlsanity.com/paper/2601.19966/) (2026)
- [An SO(3)-equivariant reciprocal-space neural potential for long-range interactions](https://mlsanity.com/paper/2603.18389/) (2026)
- [Polarizable atomic multipoles for learning long-range electrostatics](https://mlsanity.com/paper/2605.05746/) (2026)

## Abstract (arXiv)

Neural architectures that learn potential energy surfaces from molecular data have undergone fast improvement in recent years. A key driver of this success is the Message Passing Neural Network (MPNN) paradigm. Its favorable scaling with system size partly relies upon a spatial distance limit on messages. While this focus on locality is a useful inductive bias, it also impedes the learning of long-range interactions such as electrostatics and van der Waals forces. To address this drawback, we propose Ewald message passing: a nonlocal Fourier space scheme which limits interactions via a cutoff on frequency instead of distance, and is theoretically well-founded in the Ewald summation method. It can serve as an augmentation on top of existing MPNN architectures as it is computationally inexpensive and agnostic to architectural details. We test the approach with four baseline models and two datasets containing diverse periodic (OC20) and aperiodic structures (OE62). We observe robust improvements in energy mean absolute errors across all models and datasets, averaging 10% on OC20 and 16% on OE62. Our analysis shows an outsize impact of these improvements on structures with high long-range contributions to the ground truth energy.