Upcoming Seminars

Seminars are held Tuesdays and Thursdays in POB 6.304 from 3:30-5:00 pm, unless otherwise noted. Speakers include scientists, researchers, visiting scholars, potential faculty, and ICES/UT Faculty or staff. Everyone is welcome to attend. Refreshments are served at 3:15 pm.


ICES Seminar - ICES Student Forum
Wednesday, Dec 9, 2015 from 9AM to 10AM
POB 6.304

Event Update Notification: Different day/time.

A Randomized Misfit Approach for Data Reduction in Large-Scale Inverse Problems.
by Ellen Le and Aaron Myers

ICES, The University of Texas at Austin

We present a randomized misfit approach (RMA) for efficient data reduction in large-scale inverse problems. The method is a random transformation approach that generates a reduced data set via random combinations of the original data. The main idea is to first randomize the misfit and then use the sample average approximation to solve the resulting stochastic optimization problem. At the heart of our approach is the blending of the stochastic programming and the random projection theories, which brings together advances from both areas and exploits opportunities at their interfaces. This permits a more complete analysis of the RMA method that is unlikely possible using theory from either area alone. One of the main results builds upon the interplay between the Johnson-Lindenstrauss lemma and large deviation theory. In particular, the former provides sharp bounds on the reduced data dimensions for a large class of sparse random transformations, while the latter introduces a new interpretation and proof of the former. To justify the RMA approach, a detailed theoretical analysis is carried out for both linear and nonlinear inverse problems. A tight connection between the Morozov’s discrepancy principle and the Johnson-Lindenstrauss lemma is presented. This accounts for the efficacy of the RMA method in significantly reducing observation data with acceptable accuracy loss for the solution of inverse problems. Various numerical results to motivate and to verify our theoretical findings are presented for inverse problems governed by elliptic partial differential equations in one, two, and three dimensions.

Hosted by Teresa Portone and Travis Sanders


ICES Seminar - ICES Student Forum
Friday, Dec 11, 2015 from 11AM to 12PM
POB 6.304

Construction of DPG Fortin Operators For Second Order Problems
by Sriram Nagaraj and Socratis Petrides

CSEM Program, ICES

The use of “ideal” optimal test functions in a Petrov-Galerkin scheme guarantees the discrete stability of the variational problem. However, in practice, the computation of the ideal optimal test functions is computationally intractable. In this talk, we study the effect of using approximate, “practical” test functions on the stability of the DPG (discontinuous Petrov-Galerkin) method. In particular, the change in stability between the “ideal” and “practical” cases is analyzed by constructing an appropriate Fortin operator. We highlight the construction of an “optimal” DPG Fortin operator for H^1 and H(div) spaces; the continuity constant of the Fortin operator is a measure of the loss of stability between the ideal and practical DPG methods.

Our results shed light not only on the change in stability by using practical test functions, but also indicate how stability varies with the approximation order (p) and the enrichment order (\Delta p). The latter has important ramifications when one wishes to pursue local hp-adaptivity.

Hosted by Teresa Portone and Travis Sanders