Active learning strategy for excursion-set confidence regions of functional simulator outputs

2026-05-28

AI Summary

This study addresses the efficient estimation of confidence regions for outputs exceeding a prescribed threshold in simulators with random inputs and functional outputs. To this end, the authors propose a surrogate modeling approach that integrates principal component analysis with Gaussian process regression. An innovative active learning strategy based on a max-min criterion is introduced, which, combined with Karhunen–Loève expansion, enables highly efficient sampling and substantially reduces uncertainty in confidence region estimation. The method is validated on three test cases: a synthetic function, the surface pressure coefficient distribution of a hypersonic vehicle, and the glide trajectory of a reusable rocket’s first stage. In all cases, it accurately and efficiently constructs confidence regions, outperforming existing benchmark methods.

Abstract

Estimating excursion set confidence regions seeks to identify regions where a function may exceed some threshold with a given confidence level. This paper focuses on estimating such confidence regions in cases where the function has random inputs and a functional output that is returned all at once. We develop a surrogate-based approach for estimating the confidence region, combining principal component analysis and Gaussian process regression. An active learning strategy is also introduced, based on a max-min criterion that selects new samples which are likely to reduce the uncertainty in the confidence region. This strategy leverages efficient sampling of the Gaussian process through a Karhunen-Loève expansion. The proposed approach is applied to estimate the confidence regions of three case studies: a synthetic function, the surface pressure coefficient distribution of a hypersonic vehicle, and the glide-back trajectory of a reusable launcher first stage. The method demonstrates efficiency in accurately estimating the confidence region while reducing sources of modeling uncertainties. It is benchmarked against reference methods from the literature. Relevant metrics for assessing the confidence region estimation performance are discussed.

Problem

• excursion set
• confidence region
• functional output
• active learning
• uncertainty quantification

Innovation

• active learning
• excursion set
• Gaussian process regression
• functional output
• Karhunen–Loève expansion