用拉普拉斯特征基约束电势，让神经势能模型自监督学习静电作用。
Electrostatics from Laplacian Eigenbasis for Neural Network Interatomic Potentials
- 基于拉普拉斯特征基构建电势表示，强制满足离散泊松方程。
- 可自洽推导电荷分布与电势，显著提升总能量预测精度。
- 轻量插件式设计，适配现有模型且计算开销极小。
本文提出Phi-Module，一种通用的可插入模块，通过在消息传递框架中施加泊松方程约束，实现神经原子间势能对静电相互作用的自监督学习。具体地，每个原子表征被强制满足离散化的泊松方程，从而可从可学习的分子图拉普拉斯特征基系数中获得电势ϕ及对应电荷 {ho}。我们进一步推导出关键的静电能量项，显著改善总能量预测性能。该方法可无缝集成至任意现有神经势能模型，计算开销极低。结果表明，在保持超参数友好、内存高效和训练轻量的同时，嵌入第一性原理约束能大幅提升模型表现。代码将发布于https://github.com/dunnolab/phi-module。
原文摘要 · Abstract (English)
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 \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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