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The Global Active Subspace Method /

Yue, Ruilong,

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The Global Active Subspace Method /

Record Type:	Electronic resources : Monograph/item
Title/Author:	The Global Active Subspace Method // Ruilong Yue.
Author:	Yue, Ruilong,
Description:	1 electronic resource (89 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
Contained By:	Dissertations Abstracts International85-12B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30996088
ISBN:	9798382788128

The Global Active Subspace Method /
Yue, Ruilong,

The Global Active Subspace Method /Ruilong Yue. - 1 electronic resource (89 pages)

Source: Dissertations Abstracts International, Volume: 85-12, Section: B.

In this dissertation, we focus on the novel dimension reduction method and its application on sensitivity analysis. First, we introduce the Monte Carlo method, one type of surrogate model, polynomial chaos expansion, the active subspace method and global sensitivity analysis. Then, to overcome the issues when there are high-oscillated or noised components in the function, we propose a global generalization of the active subspace method. We form the algorithm, do the error analysis and establish a new type of sensitivity measure based on our method. We present numerical experiments in each section to explain the framework, and support the effectiveness of our new method.

English

ISBN: 9798382788128Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Dimension reduction

The Global Active Subspace Method /
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100 1 $a Yue, Ruilong, $e author. $0 (orcid)0009-0008-3807-8731 $3 3820909
245 1 0 $a The Global Active Subspace Method / $c Ruilong Yue.
264 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2024
300 $a 1 electronic resource (89 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
500 $a Advisors: Okten, Giray Committee members: Orozco, David ; Bao, Feng ; Zhu, Lingjiong .
502 $b Ph.D. $c The Florida State University $d 2024.
520 $a In this dissertation, we focus on the novel dimension reduction method and its application on sensitivity analysis. First, we introduce the Monte Carlo method, one type of surrogate model, polynomial chaos expansion, the active subspace method and global sensitivity analysis. Then, to overcome the issues when there are high-oscillated or noised components in the function, we propose a global generalization of the active subspace method. We form the algorithm, do the error analysis and establish a new type of sensitivity measure based on our method. We present numerical experiments in each section to explain the framework, and support the effectiveness of our new method.
546 $a English
590 $a School code: 0071
650 4 $a Mathematics. $3 515831
650 4 $a Statistics. $3 517247
650 4 $a Applied mathematics. $3 2122814
650 4 $a Theoretical physics. $3 2144760
653 $a Dimension reduction
653 $a Sensitivity analysis
653 $a Polynomial chaos
653 $a Algorithm
690 $a 0405
690 $a 0753
690 $a 0364
690 $a 0463
710 2 $a The Florida State University. $b Mathematics. $e degree granting institution. $3 3820910
720 1 $a Okten, Giray $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 85-12B.
790 $a 0071
791 $a Ph.D.
792 $a 2024
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30996088