자료유형  

 학위논문

Control Number  

0017161520

International Standard Book Number  

9798342101554

Dewey Decimal Classification Number  

530

Main Entry-Personal Name  

Alberts, Alexander.

Publication, Distribution, etc. (Imprint  

[S.l.] : Purdue University., 2024

Publication, Distribution, etc. (Imprint  

Ann Arbor : ProQuest Dissertations & Theses, 2024

Physical Description  

144 p.

General Note  

Source: Dissertations Abstracts International, Volume: 86-04, Section: B.

General Note  

Advisor: Bilionis, Ilias.

Dissertation Note  

Thesis (Ph.D.)--Purdue University, 2024.

Summary, Etc.  

요약Inverse problems in infinite dimensions are ubiquitously encountered across the scien- tific disciplines. These problems are defined by the need to reconstruct continuous fields from incomplete, noisy measurements, which oftentimes leads to ill-posed problems. Almost universally, the solutions to these problems are constructed in a Bayesian framework. How- ever, in the infinite-dimensional setting, the theory is largely restricted to the Gaussian case, and the treatment of prior physical knowledge is lacking. We develop a new framework for Bayesian reconstruction of infinite-dimensional fields which encodes our physical knowledge directly into the prior, while remaining in the continuous setting. We then prove various characteristics of the method, including situations in which the problems we study have unique solutions under our framework. Finally, we develop numerical sampling schemes to characterize the various objects involved.

Subject Added Entry-Topical Term  

Physics.

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Partial differential equations.

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Coordinate transformations.

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Success.

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Inverse problems.

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Neural networks.

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Navier-Stokes equations.

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Engineering.

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Euclidean space.

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Theorems.

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Geometry.

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Parameter estimation.

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Mathematics.

Added Entry-Corporate Name  

Purdue University.

Host Item Entry  

Dissertations Abstracts International. 86-04B.

Electronic Location and Access  

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Control Number  

joongbu:657708