# Latent Ewald summation for machine learning of long-range interactions

arXiv: https://arxiv.org/abs/2408.15165 · HTML: https://mlsanity.com/paper/2408.15165/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 40 references that are in the map.
- First posted on arXiv 27 Aug 2024.

## Builds on (most cited first, 9 of 9)

- [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)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effects](https://mlsanity.com/paper/2105.00304/) (2021)
- [Ewald-based Long-Range Message Passing for Molecular Graphs](https://mlsanity.com/paper/2303.04791/) (2023)
- [Cartesian atomic cluster expansion for machine learning interatomic potentials](https://mlsanity.com/paper/2402.07472/) (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, 26 of 26)

- [Euclidean Fast Attention -- Machine Learning Global Atomic Representations at Linear Cost](https://mlsanity.com/paper/2412.08541/) (2024)
- [A universal augmentation framework for long-range electrostatics in machine learning interatomic potentials](https://mlsanity.com/paper/2507.14302/) (2025)
- [MACE-POLAR-1: A Polarisable Electrostatic Foundation Model for Molecular Chemistry](https://mlsanity.com/paper/2602.19411/) (2026)
- [A recipe for scalable attention-based MLIPs: unlocking long-range accuracy with all-to-all node attention](https://mlsanity.com/paper/2603.06567/) (2026)
- [Learning charges and long-range interactions from energies and forces](https://mlsanity.com/paper/2412.15455/) (2024)
- [Learning from the electronic structure of molecules across the periodic table](https://mlsanity.com/paper/2510.00224/) (2025)
- [chemtrain-deploy: A parallel and scalable framework for machine learning potentials in million-atom MD simulations](https://mlsanity.com/paper/2506.04055/) (2025)
- [Spectral/Spatial Tensor Atomic Cluster Expansion with Universal Embeddings in Cartesian Space](https://mlsanity.com/paper/2509.14961/) (2025)
- [DistMLIP: A Distributed Inference Platform for Machine Learning Interatomic Potentials](https://mlsanity.com/paper/2506.02023/) (2025)
- [HollowFlow: Efficient Sample Likelihood Evaluation using Hollow Message Passing](https://mlsanity.com/paper/2510.21542/) (2025)
- [Equivariant Machine Learning Interatomic Potentials with Global Charge Redistribution](https://mlsanity.com/paper/2503.17949/) (2025)
- [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)
- [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)
- [Equivariant learning of a transferable three-dimensional classical density functional](https://mlsanity.com/paper/2608.13506/) (2026)
- [Reciprocal Space Attention for Learning Long-Range Interactions](https://mlsanity.com/paper/2510.13055/) (2025)
- [AceFF: A State-of-the-Art Machine Learning Potential for Small Molecules](https://mlsanity.com/paper/2601.00581/) (2026)
- [Machine Learning Multiscale Interactions](https://mlsanity.com/paper/2605.25710/) (2026)
- [SSLFusion: Scale & Space Aligned Latent Fusion Model for Multimodal 3D Object Detection](https://mlsanity.com/paper/2504.05170/) (2025)
- [Electrostatics from Laplacian Eigenbasis for Neural Network Interatomic Potentials](https://mlsanity.com/paper/2505.14606/) (2025)
- [Performance of universal machine-learned potentials with explicit long-range interactions in biomolecular simulations](https://mlsanity.com/paper/2508.10841/) (2025)
- [MCGM: Multi-stage Clustered Global Modeling for Long-range Interactions in Molecules](https://mlsanity.com/paper/2509.22028/) (2025)
- [Long-range electrostatics for machine learning interatomic potentials is easier than we thought](https://mlsanity.com/paper/2512.18029/) (2025)
- [Distilling latent electrostatics from foundation machine learning interatomic potentials](https://mlsanity.com/paper/2606.15001/) (2026)
- [Latent unified smooth Hamiltonians for excited state chemistry](https://mlsanity.com/paper/2609.01871/) (2026)

## Abstract (arXiv)

Machine learning interatomic potentials (MLIPs) often neglect long-range interactions, such as electrostatic and dispersion forces. In this work, we introduce a straightforward and efficient method to account for long-range interactions by learning a latent variable from local atomic descriptors and applying an Ewald summation to this variable. We demonstrate that in systems including charged and polar molecular dimers, bulk water, and water-vapor interface, standard short-ranged MLIPs can lead to unphysical predictions even when employing message passing. The long-range models effectively eliminate these artifacts, with only about twice the computational cost of short-range MLIPs.