Bayesian sequential design of computer experiments to estimate reliable sets

Romain Ait Abdelmalek-Lomenech (1, 2) , Julien Bect (1, 2) , Vincent Chabridon (3, 2) , Emmanuel Vazquez (1, 2)

1 L2S - Laboratoire des signaux et systèmes
2 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
3 EDF R&D PRISME - Performance, Risque Industriel, Surveillance pour la Maintenance et l’Exploitation

We consider an unknown multivariate function representing a system-such as a complex numerical simulator-taking both deterministic and uncertain inputs. Our objective is to estimate the set of deterministic inputs leading to outputs whose probability (with respect to the distribution of the uncertain inputs) to belong to a given set is controlled by a given threshold. To solve this problem, we propose a Bayesian strategy based on the Stepwise Uncertainty Reduction (SUR) principle to sequentially choose the points at which the function should be evaluated to approximate the set of interest. We illustrate its performance and interest in several numerical experiments.

Keywords: Gaussian processes; Active learning; Design of computer experiments; Stepwise Uncertainty Reduction; Set inversion; Uncertainty quantification

Domains: Statistics [stat]; Machine Learning [stat.ML]

Romain Ait Abdelmalek-Lomenech, Julien Bect, Vincent Chabridon, Emmanuel Vazquez. Bayesian sequential design of computer experiments to estimate reliable sets. 2022. ⟨hal-03835704⟩