SCHEDULE: NOV 10-16, 2012
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Extreme-Scale UQ for Bayesian Inverse Problems Governed by PDEs
SESSION: ACM Gordon Bell Prize I
EVENT TYPE: ACM Gordon Bell Finalists
TIME: 2:30PM - 3:00PM
SESSION CHAIR: Michael Norman
AUTHOR(S):Tan Bui-Thanh, Carsten Burstedde, Omar Ghattas, James Martin, Georg Stadler, Lucas Wilcox
Quantifying uncertainties in large-scale simulations has emerged as the central challenge facing CS&E. When the simulations require supercomputers, and uncertain parameter dimensions are large, conventional UQ methods fail. Here we address uncertainty quantification for large-scale inverse problems in a Bayesian inference framework: given data and model uncertainties, find the pdf describing parameter uncertainties. To overcome the curse-of-dimensionality of conventional methods, we exploit the fact that the data are typically informative about low-dimensional manifolds of parameter space to construct low rank approximations of the covariance matrix of the posterior pdf via a matrix-free randomized method. This results in a method that scales independently of the forward problem dimension, the uncertain parameter dimension, the data dimension, and the number of processors. We apply the method to the Bayesian solution of an inverse problem in 3D global seismic wave propagation with a million parameters, for which we observe three orders of magnitude speedups.
Michael Norman (Chair) - University of California, San Diego
Tan Bui-Thanh - University of Texas at Austin
Carsten Burstedde - University of Bonn
Omar Ghattas - University of Texas at Austin
James Martin - University of Texas at Austin
Georg Stadler - University of Texas at Austin
Lucas Wilcox - University of Texas at Austin