Multifidelity Bayesian Experimental Design to Quantify Rare-Event Statistics

In this work, we develop a multifidelity Bayesian experimental design framework to efficiently quantify the rare -event statistics of an input -to -response (ItR) system with given input probability and expensive function evaluations. The key idea here is to leverage low -fidelity samples whose responses can be computed with a cost of a certain fraction of that for high-fidelity samples, in an optimized configuration to reduce the total computational cost. To accomplish this goal, we employ a multifidelity Gaussian process as the surrogate model of the ItR function and develop a new acquisition based on which the optimized next sample can be selected in terms of its location in the sample space and the fidelity level. In addition, we develop an inexpensive analytical evaluation of the acquisition and its derivative, avoiding numerical integrations that are prohibitive for high -dimensional problems. The new method is mainly tested in a bifidelity context for a series of synthetic problems with varying dimensions, low -fidelity model accuracy, and computational costs. Compared with the single -fidelity method and the bifidelity method with a predefined fidelity hierarchy, our method consistently shows the best (or among the best) performance for all the test cases. Finally, we demonstrate the superiority of our method in solving an engineering problem of estimating rareevent statistics of ship motion in irregular waves, using computational fluid dynamics with two different grid resolutions as the high- and low -fidelity models.