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A Multifidelity Quantile-Based Approach for Confidence Sets of Random Excursion Sets with Application to Ice-Sheet Dynamics

par Bulthuis, Kevin ;Pattyn, Frank ;Arnst, Maarten
Référence SIAM/ASA Journal on Uncertainty Quantification, 8, 3, page (860-890)
Publication Publié, 2020-07-21

Article révisé par les pairs

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Résumé :

In this paper, we address uncertainty quantification of physics-based computational models whenthe quantity of interest concerns geometrical characteristics of their spatial response. Within theprobabilistic context of the random set theory, we develop the concept of confidence sets that eithercontain or are contained within an excursion set of the spatial response with a specified probabilitylevel. We seek such confidence sets in a parametric family of nested candidate sets defined as aparametric family of sublevel or superlevel sets of a membership function. We show that the problemof identifying a confidence set with a given probability level in such a parametric family is equivalentto a problem of estimating a quantile of a random variable obtained as a global extremum of themembership function over the complement of the excursion set. To construct such confidence sets,we propose a computationally efficient bifidelity method that exploits a spectral representation ofthis random variable to reduce the required number of evaluations of the computational model. Weshow the interest of this concept of confidence sets and the efficiency gain of the proposed bifidelitymethod in an illustration relevant to the retreat of the grounded portion of the Antarctic ice sheet.