Extreme-scale UQ for Bayesian inverse problems governed by PDEs

Authors:
Tan Bui-Thanh;Carsten Burstedde;Omar Ghattas;James Martin;Georg Stadler;Lucas C. Wilcox
Affiliations:
The University of Texas at Austin, Austin, TX;The University of Texas at Austin, Austin, TX and Rheinische Friedrich-Wilhelms-Universitat Bonn, Bonn, Germany;The University of Texas at Austin, Austin, TX;The University of Texas at Austin, Austin, TX;The University of Texas at Austin, Austin, TX;The University of Texas at Austin, Austin, TX and Naval Postgraduate School, Monterey, CA
Venue:
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Year:
2012

Citing 11
Cited 0

Parallel multiscale Gauss-Newton-Krylov methods for inverse wave propagation

Proceedings of the 2002 ACM/IEEE conference on Supercomputing
A 14.6 billion degrees of freedom, 5 teraflops, 2.5 terabyte earthquake simulation on the Earth Simulator

Proceedings of the 2003 ACM/IEEE conference on Supercomputing
High Resolution Forward And Inverse Earthquake Modeling on Terascale Computers

Proceedings of the 2003 ACM/IEEE conference on Supercomputing
Inverse Problem Theory and Methods for Model Parameter Estimation

Inverse Problem Theory and Methods for Model Parameter Estimation
High-frequency simulations of global seismic wave propagation using SPECFEM3D_GLOBE on 62K processors

Proceedings of the 2008 ACM/IEEE conference on Supercomputing
A high-order discontinuous Galerkin method for wave propagation through coupled elastic-acoustic media

Journal of Computational Physics
Extreme-Scale AMR

Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
Scalable Earthquake Simulation on Petascale Supercomputers

Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
Fast Algorithms for Bayesian Uncertainty Quantification in Large-Scale Linear Inverse Problems Based on Low-Rank Partial Hessian Approximations

SIAM Journal on Scientific Computing
Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions

SIAM Review
p4est: Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees

SIAM Journal on Scientific Computing

Quantified Score

Hi-index	0.00

Visualization

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.