ICCOPT 2013 Talk, Room 2.4, Monday, July 29, 16:30-18:00

 Speaker: Noemi Petra, University of Texas at Austin, USA
 Title: Computational methods for Bayesian inverse problems governed by PDEs
 Co-authors: James Martin, Georg Stadler, Omar Ghattas

Scientific Program

We address the problem of quantifying uncertainty in the solution of inverse problems governed by Stokes models of ice sheet flows within the framework of Bayesian inference. Our goal is to infer the basal sliding coefficient from surface velocity observations and prior information. Computing the maximum a posteriori (MAP) estimate of the posterior basal sliding distribution requires the solution of a large-scale optimization problem subject to the Stokes equation. The optimization problem is solved with an efficient adjoint-based Newton-conjugate gradient method, which uses first and second derivative information of the negative log posterior. The posterior probability density is explored using a stochastic Newton MCMC sampling method that employs local Gaussian approximations based on gradients and Hessians (of the log posterior) as proposal densities. The method is applied to quantify uncertainties in the inference of basal boundary conditions for ice sheet models.

 Talk in: Organized Session Mon.C.24 Computational methods for inverse problems II
 Cluster: PDE-constrained optimization

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