Spectral Methods for Uncertainty Quantification

Abstract

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 predictions.

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 approximations to tackle these difficulties.

ALIREZA DOOSTAN

University of Colorado Boulder