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This paper introduces a novel framework for quantifying model-form uncertainty in non-intrusive reduced-order models (NIROMs) by integrating a perturbative stochastic representation of reduced bases with distribution-free conformal methods. The approach effectively separates basis-induced uncertainty from regression-induced uncertainty, providing a closed-form posterior variance that enhances the reliability of predictions, especially in extrapolation scenarios. Evaluations on parametric PDE benchmarks and an industrial application show that the proposed method yields reliable uncertainty quantification that surpasses traditional Gaussian predictive variance.
Uncertainty quantification in NIROMs can now be achieved with a framework that guarantees reliable predictions even in challenging extrapolation regimes.
Non-intrusive reduced-order models (NIROMs) have become a standard tool for approximating parametric partial differential equations from computer design of experiments while significantly reducing computational costs. However, assessing the reliability of their predictions remains a major challenge, particularly in extrapolation regimes or under limited training data. In this work, we introduce a framework for quantifying model-form uncertainty in NIROMs by combining a perturbative stochastic representation of reduced bases with distribution-free conformal-type methods. Starting from a deterministic reduced basis constructed from snapshot matrices, we model uncertainty through random perturbations defined on the Stiefel manifold, directed along the discarded modes, yielding stochastic reduced-order approximations whose induced variance reflects the basis-truncation error. A transport approximation gives a closed-form posterior variance that sepa- rates basis-induced from regression-induced uncertainty, without re-training the underlying Gaussian processes. We include this posterior variance within a conformal risk control calibration framework, that provides prediction sets with coordinate miscoverage guarantees. The calibration factor produced by this framework is itself an interpretable, scalar diagnostic of the quality of the uncertainty estimate. The methodology is evaluated on parametric PDE benchmarks and an industrial tire-manufacturing calendering process. Numerical experiments demonstrate reliable, locally informative uncertainty quantification that goes beyond the Gaussian predictive variance.
