# Physics-inspired Equivariant Descriptors of Non-bonded Interactions

arXiv: https://arxiv.org/abs/2308.13208 · HTML: https://mlsanity.com/paper/2308.13208/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 63 references that are in the map.
- First posted on arXiv 25 Aug 2023.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Deep neural network solution of the electronic Schr"odinger equation](https://mlsanity.com/paper/1909.08423/) (2019)
- [Unifying machine learning and quantum chemistry -- a deep neural network for molecular wavefunctions](https://mlsanity.com/paper/1906.10033/) (2019)
- [By-passing the Kohn-Sham equations with machine learning](https://mlsanity.com/paper/1609.02815/) (2016)
- [Equivariant representations for molecular Hamiltonians and N-center atomic-scale properties](https://mlsanity.com/paper/2109.12083/) (2021)
- [Multi-scale approach for the prediction of atomic scale properties](https://mlsanity.com/paper/2008.12122/) (2020)
- [Efficient Long-Range Convolutions for Point Clouds](https://mlsanity.com/paper/2010.05295/) (2020)

## Built on by (most cited first, 14 of 14)

- [Latent Ewald summation for machine learning of long-range interactions](https://mlsanity.com/paper/2408.15165/) (2024)
- [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)
- [Learning charges and long-range interactions from energies and forces](https://mlsanity.com/paper/2412.15455/) (2024)
- [Equivariant Machine Learning Interatomic Potentials with Global Charge Redistribution](https://mlsanity.com/paper/2503.17949/) (2025)
- [Equivariant Matrix Function Neural Networks](https://mlsanity.com/paper/2310.10434/) (2023)
- [Machine-Learning Interatomic Potentials for Long-Range Systems](https://mlsanity.com/paper/2502.04668/) (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)
- [Machine learning surrogate models of many-body dispersion interactions in polymer melts](https://mlsanity.com/paper/2503.15149/) (2025)
- [Long-range electrostatics for machine learning interatomic potentials is easier than we thought](https://mlsanity.com/paper/2512.18029/) (2025)
- [The Convergence Frontier: Integrating Machine Learning and High Performance Quantum Computing for Next-Generation Drug Discovery](https://mlsanity.com/paper/2603.17790/) (2026)
- [Distilling latent electrostatics from foundation machine learning interatomic potentials](https://mlsanity.com/paper/2606.15001/) (2026)
- [Structure-Adaptive Tree Field Integrators](https://mlsanity.com/paper/2609.34025/) (2026)

## Abstract (arXiv)

One essential ingredient in many machine learning (ML) based methods for atomistic modeling of materials and molecules is the use of locality. While allowing better system-size scaling, this systematically neglects long-range (LR) effects, such as electrostatics or dispersion interaction. We present an extension of the long distance equivariant (LODE) framework that can handle diverse LR interactions in a consistent way, and seamlessly integrates with preexisting methods by building new sets of atom centered features. We provide a direct physical interpretation of these using the multipole expansion, which allows for simpler and more efficient implementations. The framework is applied to simple toy systems as proof of concept, and a heterogeneous set of molecular dimers to push the method to its limits. By generalizing LODE to arbitrary asymptotic behaviors, we provide a coherent approach to treat arbitrary two- and many-body non-bonded interactions in the data-driven modeling of matter.