Sequential design of experiments to estimate a probability of exceeding a threshold in a multi-fidelity stochastic simulator

Rémi Stroh (1, 2, 3) , Séverine Demeyer (1) , Nicolas Fischer (1) , Julien Bect (2, 3) , Emmanuel Vazquez (2, 3)

1 LNE - Laboratoire National de Métrologie et d'Essais [Trappes]
2 L2S - Laboratoire des signaux et systèmes
3 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques

In this article, we consider a stochastic numerical simulator to assess the impact of some factors on a phenomenon. The simulator is seen as a black box with inputs and outputs. The quality of a simulation, hereafter referred to as fidelity, is assumed to be tunable by means of an additional input of the simulator (e.g., a mesh size parameter): high-fidelity simulations provide more accurate results, but are time-consuming. Using a limited computation-time budget, we want to estimate, for any value of the physical inputs, the probability that a certain scalar output of the simulator will exceed a given critical threshold at the highest fidelity level. The problem is addressed in a Bayesian framework, using a Gaussian process model of the multi-fidelity simulator. We consider a Bayesian estimator of the probability, together with an associated measure of uncertainty, and propose a new multi-fidelity sequential design strategy, called Maximum Speed of Uncertainty Reduction (MSUR), to select the value of physical inputs and the fidelity level of new simulations. The MSUR strategy is tested on an example.

Keywords: Multi-fidelity; Sequential design; Bayesian analysis; Gaussian process

Domains: Computation [stat.CO]; Methodology [stat.ME]; Machine Learning [stat.ML]

Rémi Stroh, Séverine Demeyer, Nicolas Fischer, Julien Bect, Emmanuel Vazquez. Sequential design of experiments to estimate a probability of exceeding a threshold in a multi-fidelity stochastic simulator. 61th World Statistics Congress of the International Statistical Institute (ISI 2017), Jul 2017, Marrakech, Morocco. ⟨hal-01569037⟩