Many geophysical systems are characterized by complex nonlinear behavior coupling multiple physical processes over a wide range of length and time scales. Mathematical and computational models of these systems often contain numerous uncertain parameters, making high-reliability predictive modeling a challenge. Rapidly expanding volumes of observational data--along with tremendous increases in HPC capability--present opportunities to reduce these uncertainties via solution of large-scale inverse problems. Bayesian inference provides a systematic framework for inferring model parameters with associated uncertainties from (possibly noisy) data and any prior information. However, solution of Bayesian inverse problems via conventional Markov chain Monte Carlo (MCMC) methods remains prohibitive for expensive models and high-dimensional parameters, as result from discretization of infinite dimensional problems with uncertain fields. Despite the large size of observational datasets, typically they can provide only sparse information on model parameters. Based on this property we design MCMC methods that adapt to the structure of the posterior probability and exploit an effectively-reduced parameter dimension, thereby making Bayesian inference tractable for some large-scale, high-dimensional inverse problems. We discuss inverse problems for the flow of the Antarctic ice sheet, which have been solved for as many as one million uncertain parameters at a cost (measured in forward problem solves) that is independent of the parameter dimension, the data dimension, and the number of processor cores. This work is joint with Tobin Isaac, Noemi Petra, and Georg Stadler.
1:00 p.m. - 2:00 p.m. (Gaithersburg, Bldg. 221, Room B145)
11:00 a.m. - 12:00 p.m. (Boulder, VTC in 81 1116)
Dr. Omar Ghattas
Dr. Ghattas is the John A. and Katherine G. Jackson Chair in Computational Geosciences, Professor of Geological Sciences and Mechanical Engineering, and Director of the Center for Computational Geosciences in the Institute for Computational Engineering and Sciences (ICES) at The University of Texas at Austin. He is also a member of the faculty in the Computational Science, Engineering, and Mathematics (CSEM) interdisciplinary PhD program in ICES, and holds courtesy appointments in Computer Science and Biomedical Engineering. Prior to coming to UT-Austin in 2005, he was a professor at Carnegie Mellon University for 16 years. He earned BS, MS, and PhD degrees from Duke University in 1984, 1986, and 1988. Ghattas received the ACM Gordon Bell Prize in 2003 (for Special Achievement) and again in 2015 (for Scalability), and was a finalist for the 2008, 2010, and 2012 Bell Prizes. He also received the 1998 Allen Newell Medal for Research Excellence, 2004/2005 CMU College of Engineering Outstanding Research Prize, SC02 Best Technical Paper Award, SC06 HPC Analytics Challenge Award, 2008 TeraGrid Capability Computing Challenge award, XSEDE12 Best Visualization Award, 2012 Jackson School of Geosciences Joseph C. Walter Excellence Award, and Best Poster Prize at SC09 and SC14. He is a Fellow of the Society for Industrial and Applied Mathematics (SIAM).