# Polarizable atomic multipoles for learning long-range electrostatics

arXiv: https://arxiv.org/abs/2605.05746 · HTML: https://mlsanity.com/paper/2605.05746/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 125 references that are in the map.
- First posted on arXiv 7 May 2026.

## Builds on (most cited first, 17 of 17)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (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)
- [Latent Ewald summation for machine learning of long-range interactions](https://mlsanity.com/paper/2408.15165/) (2024)
- [High-performance training and inference for deep equivariant interatomic potentials](https://mlsanity.com/paper/2504.16068/) (2025)
- [Physics-inspired Equivariant Descriptors of Non-bonded Interactions](https://mlsanity.com/paper/2308.13208/) (2023)
- [A predictive machine learning force field framework for liquid electrolyte development](https://mlsanity.com/paper/2404.07181/) (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)
- [Machine learning interatomic potential can infer electrical response](https://mlsanity.com/paper/2504.05169/) (2025)
- [Learning Non-Local Molecular Interactions via Equivariant Local Representations and Charge Equilibration](https://mlsanity.com/paper/2501.19179/) (2025)
- [Design Space of Self--Consistent Electrostatic Machine Learning Interatomic Potentials](https://mlsanity.com/paper/2603.14700/) (2026)

## Built on by (most cited first, 2 of 2)

- [Distilling latent electrostatics from foundation machine learning interatomic potentials](https://mlsanity.com/paper/2606.15001/) (2026)
- [NEMORA: Neural Equivariant Multipole Operators for Long-Range Atomistic Learning](https://mlsanity.com/paper/2610.10776/) (2026)

## Abstract (arXiv)

Long-range electrostatics and polarization remain central obstacles to extending machine learning interatomic potentials (MLIPs) to ionic, polar, and interfacial systems. Here we introduce a semi-local framework for learning electrostatics from energies and forces using polarizable atomic multipoles. Local equivariant descriptors predict environment-dependent latent monopoles, dipoles, and quadrupoles, while residual non-local charge transfer and polarization are captured by non-self-consistent linear response in induced charges and dipoles. Across four diverse benchmarks and four short-range MLIP architectures, the multipole hierarchy and response terms systematically improve potential energy surface accuracy, with the largest gains in systems where long-range effects are essential. More importantly, physically meaningful electrical responses emerge without direct supervision. The learned latent multipoles yield accurate Born effective charge tensors and infrared spectra in close agreement with experiments. The induced-dipole extension introduces new capabilities: it predicts polarizabilities and thereby enables semi-quantitative Raman spectra for bulk water and hybrid MAPbI3 perovskite, as well as the essential features of the surface-specific vibrational sum-frequency generation spectrum at the water-air interface. In ferroelectric HfO2, the predicted electrical response also captures LO-TO splitting and polarization switching. This systematically improvable, physically transparent framework enables MLIPs trained on standard energy and force labels to predict polarization-sensitive observables.