Michelin-backed framework quantifies uncertainty in AI simulations with guarantees

Non-intrusive reduced-order models (NIROMs) are widely used to approximate parametric partial differential equations at a fraction of the computational cost, but their predictions often lack reliability guarantees — especially when extrapolating or training on sparse data. A new paper from Michelin and ENS Paris Saclay researchers tackles this by combining a perturbative stochastic representation of reduced bases with distribution-free conformal-type methods. The framework starts from a deterministic reduced basis constructed from snapshot matrices, then models uncertainty through random perturbations defined on the Stiefel manifold, directed along the discarded modes. This yields stochastic reduced-order approximations whose variance reflects the basis-truncation error, without needing to retrain the underlying Gaussian processes. Key to the approach is a transport approximation that produces a closed-form posterior variance, cleanly separating basis-induced uncertainty from regression-induced uncertainty.

The team integrated this variance into a conformal risk control calibration framework, providing prediction sets with coordinate miscoverage guarantees. The calibration factor doubles as an interpretable scalar diagnostic that measures the quality of the uncertainty estimate itself. The method was evaluated on parametric PDE benchmarks and a real industrial tire-manufacturing calendering process, demonstrating reliable, locally informative uncertainty quantification that goes beyond the typical Gaussian predictive variance. For engineers and data scientists working with simulation models — particularly in manufacturing, aerospace, and other high-stakes domains — this offers a practical way to trust AI-driven predictions, even in unexplored regions of the parameter space. The paper is available on arXiv (2608.03360) and marks a step toward safer, more robust surrogate modeling.