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Uncertainty quantification via codimension-one partitioning

Sullivan, T. J. and Topcu, U. and McKerns, M. and Owhadi, H. (2011) Uncertainty quantification via codimension-one partitioning. International Journal for Numerical Methods in Engineering, 85 (12). pp. 1499-1521. ISSN 0029-5981. https://resolver.caltech.edu/CaltechAUTHORS:20110315-151154130

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Abstract

We consider uncertainty quantification in the context of certification, i.e. showing that the probability of some ‘failure’ event is acceptably small. In this paper, we derive a new method for rigorous uncertainty quantification and conservative certification by combining McDiarmid's inequality with input domain partitioning and a new concentration-of-measure inequality. We show that arbitrarily sharp upper bounds on the probability of failure can be obtained by partitioning the input parameter space appropriately; in contrast, the bound provided by McDiarmid's inequality is usually not sharp. We prove an error estimate for the method (Proposition 3.2); we define a codimension-one recursive partitioning scheme and prove its convergence properties (Theorem 4.1); finally, we apply a new concentration-of-measure inequality to give confidence levels when empirical means are used in place of exact ones (Section 5).


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1002/nme.3030DOIUNSPECIFIED
http://onlinelibrary.wiley.com/doi/10.1002/nme.3030/abstractPublisherUNSPECIFIED
ORCID:
AuthorORCID
Owhadi, H.0000-0002-5677-1600
Additional Information:© 2010 John Wiley & Sons, Ltd. Received 3 March 2010; Revised 14 July 2010; Accepted 25 July 2010. Article first published online: 2 Sep. 2010. The authors wish to thank the other members of the California Institute of Technology’s Predictive Science Academic Alliance Program (PSAAP) Uncertainty Quantification Group—Ali Lashgari, Bo Li and Michael Ortiz—for many stimulating discussions. They also thank the Caltech PSAAP Experimental Science Group—in particular, Marc Adams, Leslie Lamberson and Jonathan Mihaly—for formula (23). We thank the anonymous referees for their helpful comments. Calculations for this paper were performed using the Mystic optimization framework [32]. The authors also acknowledge portions of this work developed as part of the PSAAP project, supported by the United States Department of Energy National Nuclear Security Administration under Award Number DE-FC52-08NA28613, and U. Topcu acknowledges partial support from the Boeing Corporation.
Funders:
Funding AgencyGrant Number
United States Department of Energy National Nuclear Security AdministrationDE-FC52-08NA28613
Boeing CorporationUNSPECIFIED
Subject Keywords:uncertainty quantification; certification; adaptive subdivision; concentration of measure
Issue or Number:12
Record Number:CaltechAUTHORS:20110315-151154130
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20110315-151154130
Official Citation:Sullivan, T. J., Topcu, U., McKerns, M. and Owhadi, H. (2011), Uncertainty quantification via codimension-one partitioning. International Journal for Numerical Methods in Engineering, 85: 1499–1521. doi: 10.1002/nme.3030
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:22912
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:15 Mar 2011 22:41
Last Modified:03 Oct 2019 02:41

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