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

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