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Optimal Uncertainty Quantification

Owhadi, H. and Scovel, C. and Sullivan, T. J. and McKerns, M. and Ortiz, M. (2013) Optimal Uncertainty Quantification. SIAM Review, 55 (2). pp. 271-345. ISSN 0036-1445. https://resolver.caltech.edu/CaltechAUTHORS:20130618-075057070

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Abstract

We propose a rigorous framework for uncertainty quantification (UQ) in which the UQ objectives and its assumptions/information set are brought to the forefront. This framework, which we call optimal uncertainty quantification (OUQ), is based on the observation that, given a set of assumptions and information about the problem, there exist optimal bounds on uncertainties: these are obtained as values of well-defined optimization problems corresponding to extremizing probabilities of failure, or of deviations, subject to the constraints imposed by the scenarios compatible with the assumptions and information. In particular, this framework does not implicitly impose inappropriate assumptions, nor does it repudiate relevant information. Although OUQ optimization problems are extremely large, we show that under general conditions they have finite-dimensional reductions. As an application, we develop optimal concentration inequalities (OCI) of Hoeffding and McDiarmid type. Surprisingly, these results show that uncertainties in input parameters, which propagate to output uncertainties in the classical sensitivity analysis paradigm, may fail to do so if the transfer functions (or probability distributions) are imperfectly known. We show how, for hierarchical structures, this phenomenon may lead to the nonpropagation of uncertainties or information across scales. In addition, a general algorithmic framework is developed for OUQ and is tested on the Caltech surrogate model for hypervelocity impact and on the seismic safety assessment of truss structures, suggesting the feasibility of the framework for important complex systems. The introduction of this paper provides both an overview of the paper and a self-contained minitutorial on the basic concepts and issues of UQ.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1137/10080782XDOIArticle
http://epubs.siam.org/doi/abs/10.1137/10080782XPublisherArticle
http://arxiv.org/abs/1009.0679arXivDiscussion Paper
ORCID:
AuthorORCID
Owhadi, H.0000-0002-5677-1600
Scovel, C.0000-0001-7757-3411
Ortiz, M.0000-0001-5877-4824
Additional Information:© 2013, Society for Industrial and Applied Mathematics. Received by the editors September 7, 2010; accepted for publication (in revised form) May 22, 2012; published electronically May 8, 2013. This work was partially supported by the Department of Energy National Nuclear Security Administration under award DE-FC52-08NA28613 through Caltech’s ASC/PSAAP Center for the Predictive Modeling and Simulation of High Energy Density Dynamic Response of Materials. Calculations for this paper were performed using the mystic optimization framework [60]. We thank the Caltech PSAAP Experimental Science Group—Marc Adams, Leslie Lamberson, Jonathan Mihaly, Laurence Bodelot, Justin Brown, Addis Kidane, Anna Pandolfi, Guruswami Ravichandran, and Ares Rosakis— for formula (1.5) and Figure 1.2. We thank Sydney Garstang and Carmen Sirois for proofreading the manuscript. We thank Ilse Ipsen and four anonymous referees for detailed comments and suggestions.
Funders:
Funding AgencyGrant Number
Department of Energy (DOE) National Nuclear Security AdministrationDE-FC52-08NA28613
Subject Keywords:uncertainty quantification, concentration inequalities, sensitivity analysis, Markov–Kreintype reduction theorems for generalized Chebyshev optimization problems
Issue or Number:2
Classification Code:AMS subject classifications. 60E15, 62G99, 65C50, 90C26, 60-08, 28E99
Record Number:CaltechAUTHORS:20130618-075057070
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20130618-075057070
Official Citation:Optimal Uncertainty Quantification H. Owhadi, C. Scovel, T. J. Sullivan, M. McKerns, and M. Ortiz SIAM Rev. 55-2 (2013), pp. 271-345http://dx.doi.org/10.1137/10080782X
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38962
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:18 Jun 2013 17:59
Last Modified:24 Feb 2020 10:30

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