Speaker
Description
Uncertainty quantification for complex physical systems often relies on computationally expensive numerical simulators. When execution times limit the number of feasible runs, surrogate modeling becomes essential for tasks such as sensitivity analysis, design optimization, and safety assessment. Gaussian process regression (GPR) is a leading
surrogate due to its uncertainty quantification capabilities and flexibility. However, high input dimensionality—common in industrial applications—poses significant challenges: increased computational cost, deteriorated prediction accuracy, and numerical instability in covariance estimation.
We propose a dimension reduction methodology combining statistical screening and active subspace (AS) identification to enable efficient and parsimonious GPR metamodeling in large-dimensional contexts. The approach proceeds in three stages: (1) initial variable screening via independence tests based on Hilbert-Schmidt Independence Criterion (HSIC) reduces dimensionality to a tractable scale (~20 variables), (2) a medium-dimensional GPR is fitted to estimate gradient information, from which the gradient covariance matrix and its active subspace decomposition are computed, and (3) a final parsimonious low-dimensional GPR is constructed on the identified active directions. Key methodological contributions include optimal dimension selection via cross-validation adapted to the given-data context, and covariance modeling recommendations tailored to each stage: high-regularity kernels for stable gradient estimation, and flexible kernel choices for final surrogate construction.
We illustrate the methodology on a nuclear safety application: peak cladding temperature prediction during intermediate-break loss-of-coolant accidents (IB-LOCA) using the a thermal-hydraulic code. Starting from several dozens of uncertain input parameters, our approach achieves a four-fold dimension reduction yielding a parsimonious surrogate while preserving accuracy and reliable predictive intervals.
| Special/ Invited session | Invited session FrEnbis |
|---|---|
| Classification | Both methodology and application |
| Keywords | Uncertainty quantification, Computer experiments, Surrogate model, Gaussian process regression, Active subspaces. |