Multi-fidelity Bayesian experimental design to quantify extreme-event statistics

TL;DR

This paper introduces a multi-fidelity Bayesian experimental design framework that efficiently quantifies extreme-event statistics by combining low- and high-fidelity models, reducing computational costs in complex systems.

Contribution

The paper develops a novel multi-fidelity Gaussian process-based method with an analytical acquisition function for optimal sample selection, outperforming existing approaches.

Findings

The method reduces computational costs compared to single-fidelity approaches.

It outperforms pre-defined bi-fidelity methods across synthetic test cases.

Demonstrates effectiveness in estimating extreme ship motion statistics using CFD models.

Abstract

In this work, we develop a multi-fidelity Bayesian experimental design framework to efficiently quantify the extreme-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 multi-fidelity 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 tested in a bi-fidelity context for a series of synthetic problems with varying dimensions, low-fidelity model accuracy and computational costs. Comparing with the single-fidelity method and the bi-fidelity method with a pre-defined 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 the extreme ship motion statistics in irregular waves, using computational fluid dynamics (CFD) with two different grid resolutions as the high and low fidelity models.