Title: Optimal Uncertainty Quantification

Speaker: Dr. Tim Sullivan California Institute of Technology

Date/Time:  Monday, February 21, 2011, 1:30-2:30 pm (NM)           

Location: CSRI Building/Room 90 (Sandia NM)

Brief 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, given by 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 neither implicitly imposes inappropriate assumptions nor repudiates relevant information.

Under quite general conditions, OUQ problems have finite-dimensional reductions:  this makes computational implementation possible and also yields 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 not do so when the transfer functions (or probability distributions) are imperfectly known.  Example applications of OUQ to hypervelocity impact, seismic safety assessment of truss structures, and the design of multiphase steels will be considered, suggesting the feasibility of the framework for important complex systems.

This talk is based upon joint work with Mike McKerns, Houman Owhadi and Michael Ortiz (California Institute of Technology);  Clint Scovel (Los Alamos National Laboratory);  Dominik Meyer (Technische Universitaet Muenchen); Daniel Balzani (Universitaet Duisberg-Essen);  and Florian Theil (University of Warwick)

CSRI POC: James Kamm, 505-844-1401