# Learning Non-Local Molecular Interactions via Equivariant Local Representations and Charge Equilibration

arXiv: https://arxiv.org/abs/2501.19179 · HTML: https://mlsanity.com/paper/2501.19179/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 66 references that are in the map.
- First posted on arXiv 31 Jan 2025.

## Builds on (most cited first, 23 of 23)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [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)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [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)
- [The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentials](https://mlsanity.com/paper/2205.06643/) (2022)
- [SPICE, A Dataset of Drug-like Molecules and Peptides for Training Machine Learning Potentials](https://mlsanity.com/paper/2209.10702/) (2022)
- [Ewald-based Long-Range Message Passing for Molecular Graphs](https://mlsanity.com/paper/2303.04791/) (2023)
- [So3krates: Equivariant attention for interactions on arbitrary length-scales in molecular systems](https://mlsanity.com/paper/2205.14276/) (2022)
- [Machine Learning Molecular Dynamics for the Simulation of Infrared Spectra](https://mlsanity.com/paper/1705.05907/) (2017)
- [Learning neural network potentials from experimental data via Differentiable Trajectory Reweighting](https://mlsanity.com/paper/2106.01138/) (2021)
- [Machine learning of solvent effects on molecular spectra and reactions](https://mlsanity.com/paper/2010.14942/) (2020)
- [Capturing long-range interaction with reciprocal space neural network](https://mlsanity.com/paper/2211.16684/) (2022)
- [Accurate machine learning force fields via experimental and simulation data fusion](https://mlsanity.com/paper/2308.09142/) (2023)
- [chemtrain: Learning Deep Potential Models via Automatic Differentiation and Statistical Physics](https://mlsanity.com/paper/2408.15852/) (2024)
- [Euclidean Fast Attention -- Machine Learning Global Atomic Representations at Linear Cost](https://mlsanity.com/paper/2412.08541/) (2024)
- [Predicting solvation free energies with an implicit solvent machine learning potential](https://mlsanity.com/paper/2406.00183/) (2024)
- [Neural P3M: A Long-Range Interaction Modeling Enhancer for Geometric GNNs](https://mlsanity.com/paper/2409.17622/) (2024)
- [Learning charges and long-range interactions from energies and forces](https://mlsanity.com/paper/2412.15455/) (2024)

## Built on by (most cited first, 5 of 5)

- [chemtrain-deploy: A parallel and scalable framework for machine learning potentials in million-atom MD simulations](https://mlsanity.com/paper/2506.04055/) (2025)
- [Generalization of Long-Range Machine Learning Potentials in Complex Chemical Spaces](https://mlsanity.com/paper/2512.10989/) (2025)
- [Polarizable atomic multipoles for learning long-range electrostatics](https://mlsanity.com/paper/2605.05746/) (2026)
- [ConSolv: Solvent-Conditional Machine Learning Implicit Solvent Potential](https://mlsanity.com/paper/2606.24983/) (2026)
- [Long-range electrostatics for machine learning interatomic potentials is easier than we thought](https://mlsanity.com/paper/2512.18029/) (2025)

## Abstract (arXiv)

Graph Neural Network (GNN) potentials relying on chemical locality offer near-quantum mechanical accuracy at significantly reduced computational costs. Message-passing GNNs model interactions beyond their immediate neighborhood by propagating local information between neighboring particles while remaining effectively local. However, locality precludes modeling long-range effects critical to many real-world systems, such as charge transfer, electrostatic interactions, and dispersion effects. In this work, we propose the Charge Equilibration Layer for Long-range Interactions (CELLI) to address the challenge of efficiently modeling non-local interactions. This novel architecture generalizes the classical charge equilibration (Qeq) method to a model-agnostic building block for modern equivariant GNN potentials. Therefore, CELLI extends the capability of GNNs to model long-range interactions while providing high interpretability through explicitly modeled charges. On benchmark systems, CELLI achieves state-of-the-art results for strictly local models. CELLI generalizes to diverse datasets and large structures while providing high computational efficiency and robust predictions.