Multivariate conformal uncertainty propagation in multitask atomistic simulation: Successes and pitfalls

2026-09-25

AI Summary

This study addresses the formidable challenge of uncertainty quantification across scales and computational stages in multiscale atomistic simulations. To this end, it introduces multivariate conformal prediction into chemical property modeling for the first time. By integrating Bonferroni correction, Mahalanobis distance-based hyperellipsoidal sets, conformal risk control, and custom loss functions, the proposed approach precisely calibrates predictions of physical quantities such as energy while effectively capturing error cancellation and near-symmetry characteristics. Crucially, this method enables high-fidelity uncertainty propagation to downstream macroscopic properties, including elastic constants. Furthermore, it elucidates the intricate interplay between computational protocols and conformal statistical guarantees. Ultimately, this work establishes a rigorous yet practical new paradigm for uncertainty quantification in multiscale simulations.

Abstract

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.

Problem

• uncertainty quantification
• conformal prediction
• multitask atomistic simulation
• uncertainty propagation
• error cancellation

Innovation

• Multivariate conformal prediction
• Uncertainty propagation
• Atomistic simulation
• Error cancellation
• Conformal risk control