DMS Applied Mathematics Seminar

Speaker: Habib Najm (Sandia National Lab)

Title: Uncertainty Quantification in Computational Models of Large Scale Physical Systems

Abstract: Uncertainty quantification (UQ) in large scale computational models of complex physical systems faces the two key challenges of high dimensionality and high sample computational cost. Such models often involve a large number of uncertain parameters, associated with various modeling constructions, as well as uncertain initial/boundary conditions. Exploring such high dimensional spaces typically necessitates the use of a large number of computational samples, which, given the cost of large scale computational models, is prohibitively expensive and thus infeasible.  I will discuss a set of UQ methods and a UQ workflow to address this challenge. The suite of methods includes global sensitivity analysis (GSA) with polynomial chaos (PC) regression and compressive sensing, coupled with multilevel Monte Carlo (MLMC) and/or multilevel multifidelity (MLMF) methods. The combination of these tools is often useful to reliably cut down dimensionality with feasible computational costs, identifying a lower dimensional subspace on the uncertain parameters where subsequent adaptive sparse quadrature PC methods can be employed with accurate estimation of predictive uncertainty. I will illustrate this UQ workflow on model problems and on an application involving high-speed turbulent reacting flow.