Electrostatics from Laplacian Eigenbasis for Neural Network Interatomic Potentials

• URL: http://arxiv.org/abs/2505.14606v2
• Date: Wed, 15 Oct 2025 22:34:58 GMT
• Title: Electrostatics from Laplacian Eigenbasis for Neural Network Interatomic Potentials
• Authors: Maksim Zhdanov, Vladislav Kurenkov,
• Abstract summary: We introduce Phi-Module, a universal plugin module that enforces Poisson's equation within the message-passing framework.<n>Specifically, each atom-wise representation is encouraged to satisfy a discretized Poisson's equation.<n>We then derive an electrostatic energy term, crucial for improved total energy predictions.
• Score: 9.268742966352383
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 {\phi} and corresponding charges \r{ho} 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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