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Tangent-plane uncertainty outperforms random sampling for magnetic potentials
Tangent-Plane Evidential Uncertainty in Active Learning for Magnetic Interatomic Potentials
Projecting spin-force uncertainty into the plane orthogonal to local spins creates an indicator that tracks errors and selects informative训练
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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.
