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Mathematics Colloquium

Habib Najm
Sandia National Labs

Title: Uncertainty Quantification in Large Scale Computational Models
Date: Friday, October 28, 2022
Place and Time: LOV 101, 3:05-3:55 pm


Uncertainty quantification (UQ) in large scale computational models of physical systems faces the two key challenges of high dimensionality and high computational cost. Such models often involve a large number of uncertain parameters, associated with various modeling constructions, as well as uncertain initial and boundary conditions. Exploring such high-dimensional spaces necessitates the use of a large number of computational samples, which, given the cost of large-scale computational models, is prohibitively expensive. I will discuss a set of UQ methods, and a UQ workflow, to address this challenge. The suite of methods includes global sensitivity analysis with polynomial chaos (PC) regression and compressive sensing, coupled with multilevel multifidelity methods. The combination of these tools is often useful to reliably cut-down dimensionality with feasible computational costs, identifying a lower-dimensional subspace on uncertain parameters where subsequent adaptive sparse quadrature methods can be feasibly employed to arrive at accurate resulting PC surrogate constructions. These can in turn be used for both Bayesian inference and forward uncertainty propagation purposes. I will illustrate this UQ workflow on problems of practical relevance. I will also, more generally, highlight a range of challenges in both forward and inverse UQ applications at scale.