New Guassian Process Modeling for Low-Rank and Simulated Data
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Yuchi, Henry Shaowu
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Abstract
The Gaussian process and the Gaussian distribution are two popular and powerful tools for modeling and enjoy a wide range of applications across complex scientific and engineering systems in data science. They are often utilized to provide multiple functionalities, including estimation, recovery, and uncertainty quantification. In this thesis, we investigate how the Gaussian process is integrated with the multi-fidelity framework and how matrix-variate Gaussian distribution is utilized to avail matrix completion problems. The thesis is composed of the contributions made in these two directions, which include four research topics: (i) a new experimental design approach to multi-fidelity finite element simulations; (ii) a new conglomerate multi-fidelity emulator model utilizing the Gaussian process to tackle experiments multi-dimensional fidelity parameters; (iii) a new Bayesian matrix completion model utilizing matrix-variate Gaussian process facilitating subspace estimation and uncertainty quantification; and (iv) a new information recovery framework for piezoresponse microscopy data in material science studies via low-rank matrix completion and uncertainty quantification. In these chapters, we review the current works in the respective subjects and propose new contributions to each topic using real-world applications.
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Date
2023-07-24
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Dissertation