Abstract: Omar Ghattas

University of Texas at Austin

Scalable Algorithms for Large-Scale Statistical Inverse Problems, With Application to Global Seismic Inversion

We are interested in the solution of several inverse problems in solid earth geophysics, including the inference of mantle constitutive parameters from observed plate motions, earth seismic velocities from surface seismograms, and polar ice sheet basal friction from satellite observations. Each of these inverse problems is most naturally cast as a large-scale statistical inverse problem in the framework of Bayesian inference. The complicating factors are the high-dimensional parameter spaces (due to discretization of infinite-dimensional parameter fields) and very expensive forward problems (in the form of 3D nonlinear PDEs).

Here we present a so-called stochastic Newton method in which MCMC is accelerated by constructing and sampling from a proposal density that builds a local Gaussian approximation based on local gradient and Hessian (of the log posterior) information. Hessian manipulations (inverse, square root) are made tractable by a low rank approximation that exploits the compact nature of the data misfit operator. This amounts to a reduced model of the parameter-to-observable map. We apply the method to 3D seismic inverse problems with several million parameters, illustrating the efficacy and scalability of the low rank approximation. We discuss associated issues including elastic-acoustic coupling, discontinuous Galerkin discretization, gradient and Hessian consistency, adaptivity on forest of octree meshes, and scalability on petascale and GPU-accelerated systems.

This work is joint with: Tan Bui-Thanh, Carsten Burstedde, James Martin, Georg Stadler, Lucas Wilcox


 

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