Sequential Bayesian inversion of black-box functions in presence of uncertainties

Romain Ait Abdelmalek-Lomenech (1, 2) , Julien Bect (1, 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

In engineering, many system design problems come down to finding design parameters for the system to operate under desired conditions. When time-consuming numerical simulations are used to assess the conditions of operation of such systems, it is essential to treat this problem—broadly known as "inversion"—using search methods that are very sparing in the number of simulations. With this constraint in mind, we propose here a sequential strategy for a particular robust inversion problem that we call "reliability-based inversion" (RBI), in which the system has both deterministic and uncertain inputs. In this formulation, the objective is to retrieve the set of deterministic inputs such that the probability of the outputs exceeding a given level is greater than a threshold.

Keywords: robust inversion; reliability-based inversion; sequential design; Gaussian process

Domains: Statistics [stat]

Romain Ait Abdelmalek-Lomenech, Julien Bect, Emmanuel Vazquez. Sequential Bayesian inversion of black-box functions in presence of uncertainties. MASCOT-NUM 2022, Jun 2022, Clermont-Ferrand, France. . ⟨hal-03694867⟩