A non-intrusive propagation of uncertainty based on sparse approximations
Alireza Doostan, Aerospace Engineering Sciences, University of Colorado at Boulder
Monday, February 21, 2011
4:00 p.m., room 223, Weber Bldg
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.