Conformal Risk Control for Model-Form Uncertainty in Parametric Non-Intrusive Reduced-Order Models

This paper proposes an uncertainty-quantification framework for parametric non-intrusive reduced-order models. It perturbs a deterministic reduced basis on the Stiefel manifold along discarded modes, making the resulting variance reflect basis-truncation error. A transport approximation yields a closed-form posterior variance that separates basis-induced uncertainty from Gaussian-process regression uncertainty without retraining the regressors. Conformal risk control then calibrates prediction sets with coordinate-level miscoverage guarantees. The abstract reports evaluations on parametric PDE benchmarks and an industrial tire-manufacturing calendering process, with locally informative uncertainty beyond standard Gaussian predictive variance.