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.

摘要

本文涉及（确定性或随机）多保真数值模拟器的实验顺序设计，即对所研究的物理现象或系统的模拟精度提供控制的模拟器。准确的模拟通常需要大量的计算工作，而粗略的模拟则以较低的成本获得。例如，可以通过模拟器的运行时间或计算资源的财务成本来衡量成本。在此设置中，可以组合在多个保真度级别获得的模拟结果，以便以有效的方式估计感兴趣的数量（输出的最佳值、输出超过给定阈值的概率等）。我们提出了一种新的贝叶斯顺序策略，称为逐步减少不确定性的最大速率 (MR-SUR)，该策略通过最大化预期的不确定性减少与模拟成本之间的比率来选择要执行的额外模拟。这种通用策略统一了几种现有方法，并提供了开发新方法的原则方法。我们在几个例子上评估了它的性能，包括一个计算密集型的消防安全分析问题，其中感兴趣的数量是在建筑物火灾期间超过可持续阈值的概率。并提供了开发新方法的原则方法。我们在几个例子上评估了它的性能，包括一个计算密集型的消防安全分析问题，其中感兴趣的数量是在建筑物火灾期间超过可持续阈值的概率。并提供了开发新方法的原则方法。我们在几个例子上评估了它的性能，包括一个计算密集型的消防安全分析问题，其中感兴趣的数量是在建筑物火灾期间超过可持续阈值的概率。