On Extending Multifidelity Uncertainty Quantification Methods from Non-rare to Rare Problems

Abstract

When modeling a random phenomenon (e.g. ship motions in irregular seas), data are often available from multiple sources, or models, of varying fidelity, those with higher fidelity carrying higher costs. Multifidelity uncertainty quantification (UQ) offers tools that allow using lower-fidelity and lower-cost models to inform decisions being made about high-fidelity models. With a few exceptions though, much of the focus of the multifidelity UQ literature has been on characterizing uncertainty related to averages, in the context of non-rare problems where data are available to estimate these averages directly. In this work, we extend some multifidelity UQ methods to estimation of probabilities of rare events, possibly those that have not been observed in high-fidelity data. The suggested approach is based on bivariate extreme value theory, applied to simultaneously large observations from low-fidelity and high-fidelity models. The ideas are illustrated on simulated data associated with ship motions. It is not assumed that the reader is familiar with multifidelity UQ, with the discussion focusing on the most basic setting and building naturally from the recalled methods for non-rare problems.