Tangent-Plane Evidential Uncertainty in Active Learning for Magnetic Interatomic Potentials

TL;DR

This paper introduces a physically meaningful uncertainty measure for magnetic interatomic potentials that improves active learning efficiency by better selecting informative configurations.

Contribution

It extends the evidential framework to magnetic potentials by formulating tangent-plane uncertainty, enhancing active learning for spin-dependent systems.

Findings

Uncertainty correlates strongly with prediction error.

The method outperforms random sampling in configuration selection.

Improves accuracy of energy, force, and spin-force predictions.

Abstract

Magnetic interatomic potentials need to account for coupled lattice and spin degrees of freedom, yet constructing reliable training sets remains costly because noncollinear first-principles labels are expensive. Active learning can mitigate this cost, provided that the uncertainty estimate is physically meaningful for the magnetic-response targets that drive spin reorientation. Here we extend the $\mathrm{e}^2\mathrm{IP}$ evidential framework to magnetic machine-learning interatomic potentials by formulating the projected spin-force likelihood and the corresponding epistemic uncertainty in the tangent plane orthogonal to the local spin direction. This construction prevents the uncertainty model from allocating probability mass to a radial spin component that is absent from the constrained-moment supervision. Using bulk BiFeO$_3$ and monolayer CrTe$_2$ as benchmark systems, we show that the resulting tangent-plane epistemic uncertainty indicator $U_{\mathrm{epi}}^{\mathrm{sf}}$ correlates strongly with prediction error and selects more informative configurations than random sampling, simultaneously improving energy, force, and projected spin-force accuracy. These results demonstrate a physically interpretable and data-efficient route for constructing uncertainty-aware magnetic machine-learning interatomic potentials.