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Uncertainty Quantification Using Polynomial Chaos Expansions: A Compressive Sampling Approach

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Date and time:Ìý

Tuesday, September 16, 2014 - 10:30am

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Grandview Conference Room

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Realistic analysis and design of multi-disciplinary engineering systems requires not only a fine understanding and modeling of the underlying physics and their interactions but also recognition of intrinsic uncertainties and their influences on the quantities of interest. Uncertainty Quantification (UQ) is an emerging discipline that attempts to address the latter issue: It aims at meaningful characterization of uncertainties from the available measurements, as well as efficient propagation of these uncertainties through the governing equations for a quantitative validation of model p redictions.

In this talk, I will provide a brief introduction to uncertainty propagation using spectral methods,specifically Polynomial Chaos expansions. I will then discuss numerical challenges associated with these methods when the system uncertainty is characterized by a large number of random variables. Following that, I will introduce some recent numerical developments and research opportunities based on sparse approximation via compressive sampling, specifically,Ìýl1-minimization, to tackle these difficulties. Convergence analysis and sampling strategies associates with this technique will also be discussed.

This is a joint work with Jerrad Hampton and Ji Peng from ÃÛÌÇÖ±²¥ Boulder.