Material Type  

 학위논문

 

0017161520

Date and Time of Latest Transaction  

20250211151407

ISBN  

9798342101554

DDC  

530

Author  

Alberts, Alexander.

Title/Author  

An Information Field Theory Approach to Engineering Inverse Problems.

Publish Info  

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

Publish Info  

Ann Arbor : ProQuest Dissertations & Theses, 2024

Material Info  

144 p.

General Note  

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

General Note  

Advisor: Bilionis, Ilias.

학위논문주기  

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

Abstracts/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