A latent-space extrapolation grade built into graph atomic cluster expansion foundation potentials

Abstract

Foundation machine-learning interatomic potentials cover broad configurational and chemical spaces, but their reliability can vary across the atomic environments encountered during a simulation. Here we introduce the calibrated Mahalanobis (CALM) extrapolation grade $\gamma$, a piecewise differentiable per-atom quantity integrated into GRACE foundation models and evaluated alongside energies and forces in a single model pass. We define $\gamma$ from nearest-cluster Mahalanobis distances in latent feature space, setting $\gamma=1$ from the training-distance distribution separately for each element and cluster. Controlled tests show that a normalized random projection of the invariant many-body basis detects structural and chemical extrapolation. On different foundation datasets, OMat24 and SMAX, $\gamma$ correlates with atomic force errors and separates structures with different error distributions. The CALM grade adds percent-level computational cost, and its spatial gradient guides uncertainty-biased data collection toward configurations with larger absolute force errors.