Active learning strategy for excursion-set confidence regions of functional simulator outputs
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.
Versions
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BibTeX
@misc{brunel2026active,
title = {{Active learning strategy for excursion-set confidence regions of functional simulator outputs}},
author = {Lucas Brunel and Mathieu Balesdent and Loïc Brevault and Rodolphe Le Riche and Bruno Sudret},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.29516},
eprint = {2605.29516},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.29516},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Active learning strategy for excursion-set confidence regions of functional simulator outputs
AU - Lucas Brunel
AU - Mathieu Balesdent
AU - Loïc Brevault
AU - Rodolphe Le Riche
AU - Bruno Sudret
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2605.29516
UR - https://arxiv.org/abs/2605.29516
AB - 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.
ER -