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The authors evaluate multivariate conformal prediction frameworks to calibrate joint uncertainty sets over machine-learned interatomic potentials across energies, forces, and virial stresses. Robust uncertainty quantification across multistage atomistic pipelines is historically bottlenecked by naive coordinate-wise methods that fail to account for the physical error cancellations critical to downstream material properties. The findings show that embedding correlation structures via Mahalanobis-based hyperellipsoids and conformal risk control successfully preserves these error cancellations and near-symmetries when propagating guarantees to elastic constants and vacancy formation energies.
Standard uncertainty quantification fails downstream in atomistic ML because it destroys physical error cancellations, a blind spot resolved by multivariate conformal methods that explicitly preserve cross-property correlations.
Machine learning has become the standard tool for the design of interatomic potentials which balance efficiency and accuracy, but uncertainty quantification remains an open problem. Multiscale simulations introduce an additional challenge: robust uncertainty quantification across scales. Even within one scale, computations are often multistage, producing a sequence of target quantities, each dependent on the previous, and each with some uncertainty. Conformal methods have emerged as a model agnostic framework for recalibrating surrogate predictions to produce sets which contain the truth at a user-specified rate. For multistage workflows, we require uncertainty calibration for multiple chemical properties and atomistic configurations, and we want to propagate uncertainty sets to downstream quantities of interest. Such propagation should capture the error cancellations which occur in many downstream targets in materials science; for instance, an approximate energy difference is often more accurate than individual energy predictions. We present the first exploration of multivariate conformal methods for chemical properties, including Bonferroni-corrected hyperrectangles, hyperellipsoidal sets based on the Mahalanobis distance, and custom loss functions within conformal risk control. Calibration is applied directly to predicted energies, atomic forces, and virial stresses, then propagated to elastic constants and vacancy formation energies employing a variety of commonly considered approximate protocols in materials modeling. We highlight the benefits of building correlation predictions into the conformal procedure, making it possible to build sets which capture near symmetries and error cancellation. We conclude with a discussion of the interplay of the employed approximate computational protocol and conformal guarantees.