  This article deals with the sequential design of experiments for
(deterministic or stochastic) multi-fidelity numerical simulators, that is,
simulators that offer control over the accuracy of simulation of the physical
phenomenon or system under study. Very often, accurate simulations correspond
to high computational efforts whereas coarse simulations can be obtained at a
smaller cost. In this setting, simulation results obtained at several levels of
fidelity can be combined in order to estimate quantities of interest (the
optimal value of the output, the probability that the output exceeds a given
threshold...) in an efficient manner. To do so, we propose a new Bayesian
sequential strategy called Maximal Rate of Stepwise Uncertainty Reduction
(MR-SUR), that selects additional simulations to be performed by maximizing the
ratio between the expected reduction of uncertainty and the cost of simulation.
This generic strategy unifies several existing methods, and provides a
principled approach to develop new ones. We assess its performance on several
examples, including a computationally intensive problem of fire safety analysis
where the quantity of interest is the probability of exceeding a tenability
threshold during a building fire.
