### 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 language | English (US) |
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Title of host publication | 2012 International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2012 |

DOIs | |

State | Published - 2012 |

Event | 2012 24th International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2012 - Salt Lake City, UT, United States Duration: Nov 10 2012 → Nov 16 2012 |

### Other

Other | 2012 24th International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2012 |
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Country | United States |

City | Salt Lake City, UT |

Period | 11/10/12 → 11/16/12 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

TY - GEN

T1 - Extreme-scale UQ for Bayesian inverse problems governed by PDEs

AU - Bui-Thanh, Tan

AU - Burstedde, Carsten

AU - Ghattas, Omar

AU - Martin, James

AU - Stadler, Georg

AU - Wilcox, Lucas C.

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84877696912&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84877696912&partnerID=8YFLogxK

U2 - 10.1109/SC.2012.56

DO - 10.1109/SC.2012.56

M3 - Conference contribution

AN - SCOPUS:84877696912

SN - 9781467308069

BT - 2012 International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2012

ER -