Thursday, March 5 • 15:15 - 17:15
Poster: 'Adaptive hierarchical sparse-grid integration for uncertainty quantification,' Timur Takhtaganov, Rice University

Sign up or log in to save this to your schedule, view media, leave feedback and see who's attending!

I present adaptive hierarchical sparse-grid quadrature methods for the efficient evaluation of high-dimensional integrals arising in uncertainty quantification or in optimization under uncertainty. High-dimensional integration is needed when the uncertainty in the quantities of interest (such as oil production) of systems subject to random variables (such as reservoir equations with uncertainties in the geological parameters) is quantified via statistical moments (e.g., expected value, variance) or risk measures (e.g., conditional value at risk (CVaR)).  I compare sparse-grid methods based on the tensor products of 1D integration and interpolation rules using global or local polynomials. Sparse-grid methods allow to achieve the desired level of accuracy by using much less function evaluations than full tensor product rules, thus circumventing to a certain extent the "curse of dimensionality" - an exponential growth in the number of sampling points with the increasing number of random variables. This becomes especially important when each function evaluation requires solving a PDE. Particular emphasis is put on the problems where the quantity of interest is non-smooth with respect to the random variables.   I present recent developments in the adaptive sparse-grid methods utilizing hierarchical basis functions. I compare the performance of these methods on a model problem governed by a transport equation with uncertain inputs.

Thursday March 5, 2015 15:15 - 17:15 CST
BioScience Research Collaborative 6500 Main Street, Houston, Tx 77005

Attendees (0)