Sequential design of multi-fidelity computer experiments: maximizing the rate of stepwise uncertainty reduction

TL;DR

This paper introduces a Bayesian sequential design strategy called MR-SUR for multi-fidelity simulators, optimizing the rate of uncertainty reduction relative to simulation cost to efficiently estimate quantities of interest.

Contribution

It proposes a new generic Bayesian sequential method that unifies and extends existing approaches for multi-fidelity experiment design, focusing on maximizing the rate of uncertainty reduction.

Findings

The MR-SUR strategy effectively balances accuracy and computational cost.

Application to fire safety analysis demonstrates practical efficiency.

Method outperforms some existing approaches in reducing uncertainty quickly.

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. 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.