Papers › Electrostatics from Laplacian Eigenbasis for Neural Network Interatomic Potentials
Electrostatics from Laplacian Eigenbasis for Neural Network Interatomic Potentials
Maksim Zhdanov, Vladislav Kurenkov
Recent advances in neural network interatomic potentials have emerged as a promising research direction. However, popular deep learning models often lack auxiliary constraints grounded in physical laws, which could accelerate training and improve fidelity through physics-based regularization. In this work, we introduce Φ-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 a corresponding charge density ρ 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. Experiments on the OE62 and MD22 benchmarks confirm that models combined with Φ-Module achieve robust improvements over baseline counterparts. For OE62 error reduction ranges from 4.5% to 17.8%, and for MD22, baseline equipped with Φ-Module achieves best results on 5 out of 14 cases. 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 \href{https://github.com/dunnolab/phi-module}{dunnolab/phi-module}.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections