mlsanityData to 14 Oct 2026

Electrostatics from Laplacian Eigenbasis for Neural Network Interatomic Potentials

arXiv 2505.14606 ↗First posted 20 May 2025cs.LG physics.comp-phcited by 0

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Abstract (arXiv)

In this work, we introduce Phi-Module, a universal plugin module that enforces Poisson's equation within the message-passing framework to learn electrostatic interactions in a self-supervised manner. Specifically, each atom-wise representation is encouraged to satisfy a discretized Poisson's equation, making it possible to acquire a potential φ and corresponding charges rho linked to the learnable Laplacian eigenbasis coefficients of a given molecular graph. We then derive an electrostatic energy term, crucial for improved total energy predictions. This approach integrates seamlessly into any existing neural potential with insignificant computational overhead. Our results underscore how embedding a first-principles constraint in neural interatomic potentials can significantly improve performance while remaining hyperparameter-friendly, memory-efficient, and lightweight in training. Code will be available at https://github.com/dunnolab/phi-module.

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References · 17

  1. 2016SGDR: Stochastic Gradient Descent with Warm Restartscited by 5,045
  2. 2020On the Bottleneck of Graph Neural Networks and its Practical Implicationscited by 631
  3. 2017SchNet: A continuous-filter convolutional neural network for modeling quantum interactionscited by 571
  4. 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 441
  5. 2021GemNet: Universal Directional Graph Neural Networks for Moleculescited by 343
  6. 2022Long Range Graph Benchmarkcited by 263
  7. 2022Learning Local Equivariant Representations for Large-Scale Atomistic Dynamicscited by 256
  8. 2020Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Moleculescited by 255
  9. 2023A Survey on Oversmoothing in Graph Neural Networkscited by 247
  10. 2019Show Your Work: Improved Reporting of Experimental Resultscited by 169
  11. 2023Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systemscited by 121
  12. 2023Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNscited by 117
5 more
  1. 2022Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulationscited by 95
  2. 2023Ewald-based Long-Range Message Passing for Molecular Graphscited by 46
  3. 2024Latent Ewald summation for machine learning of long-range interactionscited by 26
  4. 2022Stochastic Scaling in Loss Functions for Physics-Informed Neural Networkscited by 1
  5. 2022Enhancing Neural Network Differential Equation Solverscited by 1

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