Gauge Informed Gating for Conservative Machine Learning Interatomic Potentials

Geometrical formulations of physical interactions offer a principled perspective for incorporating nonlocal information into machine learning interatomic potentials. In this work, we introduce a gauge informed message passing framework that leverages Abelian gauge geometry to enrich a conservative graph based potential with graph wide structural information. By predicting a graph conditioned spatial connection for each atom, we compute its antisymmetric curvature and construct a gauge invariant scalar density at the formal U(1) level. This quantity is used to control an identity initialized gauge gate and a bounded graph level residual, enabling curvature-aware information exchange without replacing the underlying geometric backbone or violating energy force consistency. We further investigate a variant with Lorenz gauge fixing regularization, which constrains the learned connection through its divergence. We evaluate our framework on MPTraj and an external WBM energy prediction subset. In a preliminary single seed study near 267k optimizer steps, the gauge gated model reduces MPTraj energy MAE from 0.016082 to 0.015629 eV/atom and force component MAE from 0.055375 to 0.054794, while both gauge informed variants improve WBM energy MAE. These results demonstrate the potential of gauge curvature features as physically structured nonlocal signals for molecular and materials modeling.