Extreme-scale UQ for Bayesian inverse problems governed by PDEs

Tan Bui-Thanh, Carsten Burstedde, Omar Ghattas, James Martin, Georg Stadler, Lucas C. Wilcox

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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. We obtain a method that scales independently of the forward problem dimension, the uncertain parameter dimension, the data dimension, and the number of cores. We apply the method to the Bayesian solution of an inverse problem in 3D global seismic wave propagation with over one million uncertain earth model parameters, 630 million wave propagation unknowns, on up to 262K cores, for which we obtain a factor of over 2000 reduction in problem dimension. This makes UQ tractable for the inverse problem.

Original languageEnglish (US)
Title of host publication2012 International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2012
DOIs
StatePublished - 2012
Event2012 24th International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2012 - Salt Lake City, UT, United States
Duration: Nov 10 2012Nov 16 2012

Other

Other2012 24th International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2012
CountryUnited States
CitySalt Lake City, UT
Period11/10/1211/16/12

Fingerprint

Inverse problems
Wave propagation
Seismic waves
Supercomputers
Covariance matrix
Earth (planet)
Uncertainty

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Computer Science Applications
  • Hardware and Architecture
  • Software

Cite this

Bui-Thanh, T., Burstedde, C., Ghattas, O., Martin, J., Stadler, G., & Wilcox, L. C. (2012). Extreme-scale UQ for Bayesian inverse problems governed by PDEs. In 2012 International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2012 [6468442] https://doi.org/10.1109/SC.2012.56

Extreme-scale UQ for Bayesian inverse problems governed by PDEs. / Bui-Thanh, Tan; Burstedde, Carsten; Ghattas, Omar; Martin, James; Stadler, Georg; Wilcox, Lucas C.

2012 International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2012. 2012. 6468442.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Bui-Thanh, T, Burstedde, C, Ghattas, O, Martin, J, Stadler, G & Wilcox, LC 2012, Extreme-scale UQ for Bayesian inverse problems governed by PDEs. in 2012 International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2012., 6468442, 2012 24th International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2012, Salt Lake City, UT, United States, 11/10/12. https://doi.org/10.1109/SC.2012.56
Bui-Thanh T, Burstedde C, Ghattas O, Martin J, Stadler G, Wilcox LC. Extreme-scale UQ for Bayesian inverse problems governed by PDEs. In 2012 International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2012. 2012. 6468442 https://doi.org/10.1109/SC.2012.56
Bui-Thanh, Tan ; Burstedde, Carsten ; Ghattas, Omar ; Martin, James ; Stadler, Georg ; Wilcox, Lucas C. / Extreme-scale UQ for Bayesian inverse problems governed by PDEs. 2012 International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2012. 2012.
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