Uncertainty Quantification for Underdetermined Inverse Problems via Krylov Subspace Iterative Solvers

Uncertainty Quantification for Underdetermined Inverse Problems via Krylov Subspace Iterative Solvers

Bibliographic Details
Main Author: Devathi, Duttaabhinivesh
Language:English
Published: Case Western Reserve University School of Graduate Studies / OhioLINK 2019
Subjects:
Applied Mathematics
uncertainty quantification
bayesian
inverse problem
machine learning
sampling
Online Access:http://rave.ohiolink.edu/etdc/view?acc_num=case155446130705089
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spelling ndltd-OhioLink-oai-etd.ohiolink.edu-case1554461307050892021-08-03T07:09:58Z Uncertainty Quantification for Underdetermined Inverse Problems via Krylov Subspace Iterative Solvers Devathi, Duttaabhinivesh Applied Mathematics uncertainty quantification bayesian inverse problem machine learning sampling In the Bayesian framework, inverse problems can be recast as statistical inference problems, in which the noisy observations are used to update the prior beliefs about the unknowns, encoded in the prior distribution. The Bayesian solution to an inverse problem is thus the posterior distribution. While in the traditional deterministic setting a solution to an inverse problem was given by a single regularized estimate, in the statistical setting uncertainty quantification, by exploring the posterior via sampling strategies, is a central task. The topic of this thesis is to investigate the approximation of the posterior distribution by a sample obtained by using Krylov subspace iterative solvers. It is well known that the Bayesian maximum a posteriori estimate is related to the classical Tikhonov regularized solution, and is effectively approximated with iterative solvers equipped with an early stopping criterion. The novelty of this work is to use the latter ones for posterior sampling: a particularly promising direction is to use priorconditioners, or statistically inspired preconditioners, to embed the prior information in the iterative solvers. In that context we have tested different sampling approaches, equipped with a novel early stopping criterion and demonstrate the viability of the approach by computed examples. 2019-05-23 English text Case Western Reserve University School of Graduate Studies / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=case155446130705089 http://rave.ohiolink.edu/etdc/view?acc_num=case155446130705089 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.
collection NDLTD
language English
sources NDLTD
topic Applied Mathematics
uncertainty quantification
bayesian
inverse problem
machine learning
sampling
spellingShingle Applied Mathematics
uncertainty quantification
bayesian
inverse problem
machine learning
sampling
Devathi, Duttaabhinivesh
Uncertainty Quantification for Underdetermined Inverse Problems via Krylov Subspace Iterative Solvers
author Devathi, Duttaabhinivesh
author_facet Devathi, Duttaabhinivesh
author_sort Devathi, Duttaabhinivesh
title Uncertainty Quantification for Underdetermined Inverse Problems via Krylov Subspace Iterative Solvers
title_short Uncertainty Quantification for Underdetermined Inverse Problems via Krylov Subspace Iterative Solvers
title_full Uncertainty Quantification for Underdetermined Inverse Problems via Krylov Subspace Iterative Solvers
title_fullStr Uncertainty Quantification for Underdetermined Inverse Problems via Krylov Subspace Iterative Solvers
title_full_unstemmed Uncertainty Quantification for Underdetermined Inverse Problems via Krylov Subspace Iterative Solvers
title_sort uncertainty quantification for underdetermined inverse problems via krylov subspace iterative solvers
publisher Case Western Reserve University School of Graduate Studies / OhioLINK
publishDate 2019
url http://rave.ohiolink.edu/etdc/view?acc_num=case155446130705089
work_keys_str_mv AT devathiduttaabhinivesh uncertaintyquantificationforunderdeterminedinverseproblemsviakrylovsubspaceiterativesolvers
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