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Gradient-Free Active Subspace Constr...

Lewis, Allison Leigh.

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Gradient-Free Active Subspace Construction and Model Calibration Techniques for Complex Models.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Gradient-Free Active Subspace Construction and Model Calibration Techniques for Complex Models./
作者:	Lewis, Allison Leigh.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2016,
面頁冊數:	130 p.
附註:	Source: Dissertation Abstracts International, Volume: 78-08(E), Section: B.
Contained By:	Dissertation Abstracts International78-08B(E).
標題:	Applied mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10583456
ISBN:	9781369621358

Gradient-Free Active Subspace Construction and Model Calibration Techniques for Complex Models.
Lewis, Allison Leigh.

Gradient-Free Active Subspace Construction and Model Calibration Techniques for Complex Models. - Ann Arbor : ProQuest Dissertations & Theses, 2016 - 130 p.

Source: Dissertation Abstracts International, Volume: 78-08(E), Section: B.

Thesis (Ph.D.)--North Carolina State University, 2016.

As physical models used in large-scale applications become increasingly complex and computationally demanding, numerous issues related to the field of uncertainty quantification (UQ) must be addressed. Knowledge of topics such as model calibration, parameter selection, uncertainty propagation, and surrogate modeling have become essential to researchers in a wide array of fields. In this dissertation, we focus on two aspects of UQ: (i) model calibration in a high-to-low-fidelity framework, and (ii) gradient-free construction of active subspaces for emulation via response surfaces.

ISBN: 9781369621358Subjects--Topical Terms:

2122814
Applied mathematics.

Gradient-Free Active Subspace Construction and Model Calibration Techniques for Complex Models.
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500 $a Source: Dissertation Abstracts International, Volume: 78-08(E), Section: B.
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520 $a As physical models used in large-scale applications become increasingly complex and computationally demanding, numerous issues related to the field of uncertainty quantification (UQ) must be addressed. Knowledge of topics such as model calibration, parameter selection, uncertainty propagation, and surrogate modeling have become essential to researchers in a wide array of fields. In this dissertation, we focus on two aspects of UQ: (i) model calibration in a high-to-low-fidelity framework, and (ii) gradient-free construction of active subspaces for emulation via response surfaces.
520 $a We first develop an information-theoretic approach to calibrating low-fidelity codes using simulated data from validated high-fidelity models, which are prohibitively expensive to evaluate repeatedly. Our objective is to employ a minimal number of high-fidelity code evaluations as synthetic data for Bayesian calibration of the low-fidelity code under consideration. We employ the mutual information between low-fidelity model parameters and experimental designs to determine input values to the high-fidelity code, which maximize the available information. For computationally expensive codes, surrogate models may be used to approximate the mutual information. We illustrate this framework using a comprehensive set of numerical examples, including several relevant to nuclear power plant design.
520 $a Recent developments in the field of reduced-order modeling---and in particular, active subspace construction---have made it possible to efficiently approximate complex models by constructing loworder response surfaces based upon a small subspace of the original high-dimensional parameter space. These methods rely upon the fact that the response tends to vary more prominently in a few dominant directions defined by linear combinations of the original inputs, allowing for a rotation of the coordinate axis and a consequent transformation of the parameters. In the second portion of this dissertation, we analyze existing gradient-based methods for active subspace construction, and propose a gradient-free active subspace algorithm that is feasible for high-dimensional parameter spaces where finite-difference techniques are impractical. These algorithms are illustrated with several examples from aerospace and nuclear engineering, with input spaces of up to 7700 dimensions.
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