Owhadi, H. and Scovel, C. and Sullivan, T. J. and McKerns, M. and Ortiz, M. (2010) Optimal Uncertainty Quantification. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20111012113158874

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Abstract
We propose a rigorous framework for Uncertainty Quantification (UQ) in which the UQ objectives and the 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 extreme values of welldefined 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 finitedimensional reductions. As an application, we develop Optimal Concentration Inequalities (OCI) of Hoeffding and McDiarmid type. Surprisingly, contrary to the classical sensitivity analysis paradigm, these results show that uncertainties in input parameters do not necessarily propagate to output uncertainties. In addition, a general algorithmic framework is developed for OUQ and is tested on the Caltech surrogate model for hypervelocity impact, suggesting the feasibility of the framework for important complex systems.
Item Type:  Report or Paper (Technical Report)  

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Additional Information:  The authors gratefully acknowledge portions of this work supported by the Department of Energy National Nuclear Security Administration under Award Number DEFC52 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 [33]. 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 (5.1). We thank Sydney Garstang for proofreading the manuscript.  
Group:  Applied & Computational Mathematics  
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Record Number:  CaltechAUTHORS:20111012113158874  
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:20111012113158874  
Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  27192  
Collection:  CaltechACMTR  
Deposited By:  Kristin Buxton  
Deposited On:  19 Oct 2011 19:48  
Last Modified:  24 Feb 2016 02:21 
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