Jackknife-conformal uncertainty for linear ACE potentials: calibrated forces and silicon properties compared with Bayesian and POPS baselines

Abstract

Machine-learned interatomic potentials are misspecified, so Bayesian posterior variances understate their errors. For linear atomic cluster expansion (ACE) potentials we derive calibrated uncertainties from one misspecification-robust parameter covariance, the delete-one-configuration jackknife. Scaled by one conformal quantile from a held-out part of the training set, it gives per-atom force uncertainties close to their target coverage on held-out silicon data and on cracks left out of the fit; screw dislocations left out are under-covered by the smaller of the two models. With one scale fitted to the forces of a held-out test split, the same parameter distribution is propagated to 21 properties of silicon, from elastic constants to defect and surface energies, by implicit differentiation through each relaxation and by committees, and is tested against density functional theory (DFT) without tuning on any property. For a smaller and a larger model the intervals cover most properties, and the larger model's are about 4 times tighter. The Bayesian posterior with one calibrated scale has the wrong shape: it covers fewer properties and has far lower joint evidence. Pointwise optimal parameter sets (POPS), once their hypercube is numerically defined, performs comparably on the properties, but its per-atom force regions are not calibrated to a target (0.95 and 0.84 at a nominal 0.90). Where the jackknife fails is relaxed point defects, whose training cells are all hot snapshots: a bias that every configuration shares is invisible to a jackknife, but it can be measured from the training labels, and as a discrepancy term, devised after the property results were seen, it brings the coverage close to nominal.