Sequential design of multi-fidelity computer experiments: maximizing the rate of stepwise uncertainty reduction
This work addresses the challenge of optimizing computational resources in multi-fidelity simulations for applications like fire safety, though it appears incremental as it unifies existing methods.
The paper tackles the problem of efficiently designing multi-fidelity computer experiments by proposing MR-SUR, a Bayesian sequential strategy that maximizes the ratio of uncertainty reduction to simulation cost, and demonstrates its performance on examples including a fire safety analysis.
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.