Sequential Design of Multi-Fidelity Computer Experiments: Maximizing the Rate of Stepwise Uncertainty Reduction

Abstract

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. Accurate simulations usually entail a high computational effort, while coarse simulations are obtained at a lower cost. The cost can be measured, for example, by the run time of the simulator or the financial cost of the computing resources. 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, etc.) in an efficient manner. 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.

KEYWORDS:

• Computer experiments
• Gaussian process emulator
• Meta-model
• Surrogate model
• Multi-fidelity
• Sequential design of experiments
• Stochastic simulator

Supplementary Material

Complementary information: Generalization and proof of the SUR sampling criterion (11), a short bibliography about nonsequential multi-fidelity designs, and more detailed information regarding the numerical experiments. (PDF file)

Source code: Matlab programs to reproduce the numerical experiments of Section 3.3, 4.2, and 4.3, including the modified version of the STK toolbox for Matlab/Octave (Bect et al. 2017) that was used for these experiments.

Additional information

Funding

This work was supported by the French Association Nationale de la Recherche et de la Technologie (ANRT) under grant CIFRE 2014/1350.