Many industrial problems require the use of black-box numerical simulators, for which it is essential to determine the set of so-called feasible input parameters. A set of parameters is feasible if the output of the code on these parameters satisfies given constraints, for example, by remaining below a certain threshold. Active learning is an effective approach to solve this type of problem, by sequentially enriching a design of experiments using a well-chosen acquisition criterion, based here on a Gaussian process surrogate model. In this work, we focus specifically on simulators with vector outputs. We propose several enrichment strategies to simultaneously explore the entire collection of feasible sets associated with each output component. These enrichment strategies are first tested and compared on analytical test functions, before being applied to the pre-calibration of a simulator dedicated to wind turbine design. The aim is to identify input parameter configurations that respect the vibration constraints imposed on the simulator outputs. Numerical results demonstrate the efficiency of the three proposed strategies, which are compared against two baseline strategies (random sampling and Sobol’ sequence).
Keywords: Gaussian process regression, excursion set estimation, multi-output black-box functions, active learning, sequential design of experiments
Clément Duhamel 1 ; Céline Helbert 2 ; Miguel Munoz Zuniga 3 ; Clémentine Prieur 1 ; Delphine Sinoquet 3
Clément Duhamel; Céline Helbert; Miguel Munoz Zuniga; Clémentine Prieur; Delphine Sinoquet. Active learning strategies for the estimation of a feasible set defined from a vector output black-box simulator. The SMAI Journal of computational mathematics, Volume 12 (2026), pp. 331-369. doi: 10.5802/smai-jcm.151
@article{SMAI-JCM_2026__12__331_0,
author = {Cl\'ement Duhamel and C\'eline Helbert and Miguel Munoz Zuniga and Cl\'ementine Prieur and Delphine Sinoquet},
title = {Active learning strategies for the estimation of a feasible set defined from a vector output black-box simulator},
journal = {The SMAI Journal of computational mathematics},
pages = {331--369},
year = {2026},
publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
volume = {12},
doi = {10.5802/smai-jcm.151},
language = {en},
url = {https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.151/}
}
TY - JOUR AU - Clément Duhamel AU - Céline Helbert AU - Miguel Munoz Zuniga AU - Clémentine Prieur AU - Delphine Sinoquet TI - Active learning strategies for the estimation of a feasible set defined from a vector output black-box simulator JO - The SMAI Journal of computational mathematics PY - 2026 SP - 331 EP - 369 VL - 12 PB - Société de Mathématiques Appliquées et Industrielles UR - https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.151/ DO - 10.5802/smai-jcm.151 LA - en ID - SMAI-JCM_2026__12__331_0 ER -
%0 Journal Article %A Clément Duhamel %A Céline Helbert %A Miguel Munoz Zuniga %A Clémentine Prieur %A Delphine Sinoquet %T Active learning strategies for the estimation of a feasible set defined from a vector output black-box simulator %J The SMAI Journal of computational mathematics %D 2026 %P 331-369 %V 12 %I Société de Mathématiques Appliquées et Industrielles %U https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.151/ %R 10.5802/smai-jcm.151 %G en %F SMAI-JCM_2026__12__331_0
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