Scientific Computing Group Seminars - Detail View

Speaker: A. Doostan

Affiliation: University of Colorado at Boulder

Talk Title: A Compressive Sampling Approach to Uncertainty Propagation

Invited by: George Karniadakis

Time: Nov. 18 2011 11 a.m.

Location: 182 George Street, room 110

Abstract:

Uncertainty quantification (UQ) is an inevitable part of any predictive modeling practice. Intrinsic variabilities and lack of knowledge about system parameters or governing physical models often considerably affect quantities of interest and decision-making processes. Efficient representation and propagation of such uncertainties through complex PDE systems are subjects of growing interests, especially for situations where a large number of uncertain sources are present. One major difficulty in UQ of such systems is the development of non-intrusive approaches in which deterministic codes are used in a black box fashion, and at the same time, solution structures are exploited to reduce the number of deterministic runs. Here we extend ideas from compressive sampling techniques to approximate solutions of PDEs with stochastic inputs using direct, i.e., non-adapted, sampling of solutions. This sampling can be done by using any legacy code for the deterministic problem as a black box. The method converges in probability (with probabilistic error bounds) as a consequence of sparsity of solutions and a concentration of measure phenomenon on the empirical correlation between samples. We show that the method is well suited for PDEs with high-dimensional stochastic inputs. This is a joint work with Prof. Houman Owhadi from California Institute of Technology.