A Multifidelity Quantile-Based Approach for Confidence Sets of Random Excursion Sets with Application to Ice-Sheet Dynamics
peer reviewed In this paper, we address uncertainty quantification of physics-based computational models when the quantity of interest concerns geometrical characteristics of their spatial response. Within the probabilistic context of the random set theory, we develop the concept of confidence sets...
| Published in: | SIAM/ASA Journal on Uncertainty Quantification |
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| Main Authors: | , , |
| Format: | Article in Journal/Newspaper |
| Language: | English |
| Published: |
Society for Industrial and Applied Mathematics (SIAM)
2020
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| Subjects: | |
| Online Access: | https://orbi.uliege.be/handle/2268/249728 https://doi.org/10.1137/19M1280466 |
| Summary: | peer reviewed In this paper, we address uncertainty quantification of physics-based computational models when the quantity of interest concerns geometrical characteristics of their spatial response. Within the probabilistic context of the random set theory, we develop the concept of confidence sets that either contain or are contained within an excursion set of the spatial response with a specified probability level. We seek such confidence sets in a parametric family of nested candidate sets defined as a parametric family of sublevel or superlevel sets of a membership function. We show that the problem of identifying a confidence set with a given probability level in such a parametric family is equivalent to a problem of estimating a quantile of a random variable obtained as a global extremum of the membership 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 of this random variable to reduce the required number of evaluations of the computational model. We show the interest of this concept of confidence sets and the efficiency gain of the proposed bifidelity method in an illustration relevant to the retreat of the grounded portion of the Antarctic ice sheet. Dans ce papier, nous nous intéressons à la quantification d'incertitudes dans des modèles numériques à caractère physique pour lesquels la quantité d'intérêt concerne les caractéristiques géométriques de leur réponse spatiale. Dans le cadre probabiliste de la théorie des ensembles aléatoires, nous développons le concept d'ensembles de confiance qui contiennent ou sont contenus dans un ensemble d'excursion de la réponse spatiale avec un niveau donné de probabilité. Nous cherchons de tels ensembles de confiance dans une famille paramétrique d'ensembles candidats imbriqués définie comme une famille de surniveaux ou de sous-niveaux d'une fonction d'appartenance. Nous montrons que l'identification d'un ensemble de confiance ... |
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