DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:**Kevin Carlberg, Sandia

**Title: ***
Reduced-order modeling in uncertainty quantification: modeling and controlling error
*

**Abstract:**
Many tasks in uncertainty quantification require hundreds or thousands of `forward' model simulations. In Bayesian inversion, for example, each sample from the posterior distribution requires (at least) one forward simulation. Employing high-fidelity, large scale computational models for such tasks is infeasible, as a single simulation can consume days or weeks on a supercomputer.
To make such problems tractable, we 1) replace the large-scale model with a low-dimensional reduced-order model (ROM), 2) rigorously account for the additional (epistemic) uncertainty introduced by the ROM, and 3) control this uncertainty by adaptively refining the ROM as needed.
Two newly developed methods enable this strategy. For step 2 above, we propose the ROMES method, which employs stochastic processes to construct accurate statistical models of the ROM error. For step 3, we propose an adaptive h-refinement approach that borrows many concepts from mesh adaptation in finite elements.

**Time:** Friday, April 25, 2014, 1:30-2:30 p.m.

**Place:** Exploratory Hall (formerly S & T II), Room 4106

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491