NDLI: Research Spotlights (SIREAD Vol. 55 Issue. 2)

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Research Spotlights (SIREAD Vol. 55 Issue. 2)

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Tuminaro, Ray
Copyright Year	2013
Abstract	This issue's Research Spotlights article by Owhadi, Scovel, Sullivan, McKerns, and Ortiz highlights one of the key challenges associated with uncertainty quantification (UQ): a disconnect between theoretical UQ methods and complex systems of importance ... in the sense that the assumptions of the methods do not match the assumption/information set of the application. From a broader perspective, the paper argues that there is a lack of universally accepted UQ objectives or even standards for communicating results. The article Optimal Uncertainty Quantification proposes a rigorous framework for UQ which is based on optimizing a functional that incorporates problem constraints, problem knowledge, and a lack of available information. This approach is referred to as optimal uncertainty quantification (OUC). Of course in the most general situations, the resulting optimization problems are infinite-dimensional and nonconvex, and so they cannot be solved directly. For an important subclass, however, the authors show that the resulting optimization problem can be solved by reducing it to a finite convex combination of extreme points. This is illustrated concretely for a physical model corresponding to hypervelocity impact of a ball fired at a plate using data from experiments at the Cal Tech Small Particle Hypervelocity Impact Range facility. More importantly, these results are generalized in the form of a reduction theorem which defines the subclass and outlines a reduction technique which can lead to practical and simplified optimization problems. One intriguing aspect of the proposed theory is a nonpropagation of uncertainties. That is, the optimal bounds may not depend on uncertainties in some input parameters when incomplete information associated with response functions and probability measures is considered, even though there may have been a dependence when this incomplete information was ignored. As the authors note, optimal uncertainty quantification is not the definitive answer to the above-mentioned disconnect, but it will hopefully stimulate further discussions concerning the need for and development of a rigorous UQ framework.
Starting Page	269
Ending Page	269
Page Count	1
File Format	PDF
ISSN	00361445
DOI	10.1137/130973387
e-ISSN	10957200
Journal	SIAM Review (SIREAD)
Issue Number	2
Volume Number	55
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2013-01-01
Access Restriction	Subscribed
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Computational Mathematics

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