Bayesian sequential design of computer experiments for quantile set inversion

• URL: http://arxiv.org/abs/2211.01008v6
• Date: Thu, 22 Aug 2024 08:24:57 GMT
• Title: Bayesian sequential design of computer experiments for quantile set inversion
• Authors: Romain Ait Abdelmalek-Lomenech, Julien Bect, Vincent Chabridon, Emmanuel Vazquez,
• Abstract summary: We consider an unknown multivariate function representing a system-such as a complex numerical simulator. Our objective is to estimate the set of deterministic inputs leading to outputs whose probability is less than a given threshold.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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) of belonging to a given set is less than a given threshold. This problem, which we call Quantile Set Inversion (QSI), occurs for instance in the context of robust (reliability-based) optimization problems, when looking for the set of solutions that satisfy the constraints with sufficiently large probability. To solve the QSI problem we propose a Bayesian strategy, based on Gaussian process modeling and the Stepwise Uncertainty Reduction (SUR) principle, to sequentially choose the points at which the function should be evaluated to efficiently approximate the set of interest. We illustrate the performance and interest of the proposed SUR strategy through several numerical experiments.

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