Electrostatics from Laplacian Eigenbasis for Neural Network Interatomic Potentials

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 $\boldsymbol{\phi}$ and a corresponding charge density $\boldsymbol{\rho}$ 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.