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You searched for +publisher:"University of Texas – Austin" +contributor:("Marzouk, Youssef"). One record found.

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University of Texas – Austin

1. -0613-6243. A computational framework for the solution of infinite-dimensional Bayesian statistical inverse problems with application to global seismic inversion.

Degree: Computational Science, Engineering, and Mathematics, 2015, University of Texas – Austin

Quantifying uncertainties in large-scale forward and inverse PDE simulations has emerged as a central challenge facing the field of computational science and engineering. The promise of modeling and simulation for prediction, design, and control cannot be fully realized unless uncertainties in models are rigorously quantified, since this uncertainty can potentially overwhelm the computed result. While statistical inverse problems can be solved today for smaller models with a handful of uncertain parameters, this task is computationally intractable using contemporary algorithms for complex systems characterized by large-scale simulations and high-dimensional parameter spaces. In this dissertation, I address issues regarding the theoretical formulation, numerical approximation, and algorithms for solution of infinite-dimensional Bayesian statistical inverse problems, and apply the entire framework to a problem in global seismic wave propagation. Classical (deterministic) approaches to solving inverse problems attempt to recover the “best-fit” parameters that match given observation data, as measured in a particular metric. In the statistical inverse problem, we go one step further to return not only a point estimate of the best medium properties, but also a complete statistical description of the uncertain parameters. The result is a posterior probability distribution that describes our state of knowledge after learning from the available data, and provides a complete description of parameter uncertainty. In this dissertation, a computational framework for such problems is described that wraps around the existing forward solvers, as long as they are appropriately equipped, for a given physical problem. Then a collection of tools, insights and numerical methods may be applied to solve the problem, and interrogate the resulting posterior distribution, which describes our final state of knowledge. We demonstrate the framework with numerical examples, including inference of a heterogeneous compressional wavespeed field for a problem in global seismic wave propagation with 10⁶ parameters. Advisors/Committee Members: Ghattas, Omar N. (advisor), Biros, George (committee member), Demkowicz, Leszek (committee member), Fomel, Sergey (committee member), Marzouk, Youssef (committee member), Moser, Robert (committee member).

Subjects/Keywords: Bayesian inference; Infinite-dimensional inverse problems; Uncertainty quantification; Low-rank approximation; Optimality; Scalable algorithms; High performance computing; Markov chain Monte Carlo; Stochastic Newton; Seismic wave propagation

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APA (6th Edition):

-0613-6243. (2015). A computational framework for the solution of infinite-dimensional Bayesian statistical inverse problems with application to global seismic inversion. (Thesis). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/31374

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

-0613-6243. “A computational framework for the solution of infinite-dimensional Bayesian statistical inverse problems with application to global seismic inversion.” 2015. Thesis, University of Texas – Austin. Accessed May 23, 2019. http://hdl.handle.net/2152/31374.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

-0613-6243. “A computational framework for the solution of infinite-dimensional Bayesian statistical inverse problems with application to global seismic inversion.” 2015. Web. 23 May 2019.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Vancouver:

-0613-6243. A computational framework for the solution of infinite-dimensional Bayesian statistical inverse problems with application to global seismic inversion. [Internet] [Thesis]. University of Texas – Austin; 2015. [cited 2019 May 23]. Available from: http://hdl.handle.net/2152/31374.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

-0613-6243. A computational framework for the solution of infinite-dimensional Bayesian statistical inverse problems with application to global seismic inversion. [Thesis]. University of Texas – Austin; 2015. Available from: http://hdl.handle.net/2152/31374

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Not specified: Masters Thesis or Doctoral Dissertation

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