Friday, April 18, 2014 4:00 p.m. ETC 4.150
Professor Omar Ghattas
Department of Mechanical Engineering and Department of Geological Sciences
Director of the Center for Computational Geosciences
Institute for Computational Engineering and Sciences
The University of Texas at Austin
Inverse problems governed by wave propagation–in which we seek to reconstruct the unknown shape of a scatterer, or the unknown properties of a medium, from observations of waves that are scattered by the shape or medium–play an important role in a number of engineered or natural systems. We formulate the inverse problem in the framework of Bayesian inference. This provides a systematic and coherent treatment of uncertainties in all components of the inverse problem, from observations to prior knowledge to the wave propagation model, yielding the uncertainty in the inferred medium/shape in a systematic and consistent manner. Unfortunately, state-ofthe-art Markov chain Monte Carlo methods for characterizing the solution of Bayesian inverse problems are prohibitive when the forward problem is of large scale (as in our 100-1000 wavelength target problems) and a high-dimensional parameterization is employed to describe the unknown medium (as in our target problems involving infinite-dimensional medium/shape fields, which result in millions of parameters when discretized). We report on recent research aimed at overcoming the mathematical and computational barriers for large-scale Bayesian inverse wave propagation problems. These include:
- a high order, parallel, adaptive hp-non-conforming discontinuous Galerkin (DG) method for acoustic/elastic/electromagnetic wave propagation
- infinite-dimensional formulations of Bayesian inverse problems and their consistent finite-dimensional discretizations;
- a stochastic Newton MCMC method for solution of the statistical inverse problem that reduces the number of samples needed by several orders of magnitude, relative to conventional MCMC;
- fast low rank randomized SVD approximation of the Hessian based on compactness properties; and
- applications to Bayesian inverse wave propagation in whole Earth seismology with up to one million earth model parameters, 630 million state variables, on up to 100,000 processors.
This work is joint with George Biros, Tan Bui-Thanh, Carsten Burstedde, James Martin, Georg Stadler, Hari Sundar, and Lucas Wilcox.