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Graph Related Data Analysis and Neural Network Based Partial Differential Equations Solver.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Graph Related Data Analysis and Neural Network Based Partial Differential Equations Solver./
Author:	Hu, Ziqing.
Description:	1 online resource (134 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 84-08, Section: B.
Contained By:	Dissertations Abstracts International84-08B.
Subject:	Applied mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9798368444437

Graph Related Data Analysis and Neural Network Based Partial Differential Equations Solver.
Hu, Ziqing.

Graph Related Data Analysis and Neural Network Based Partial Differential Equations Solver. - 1 online resource (134 pages)

Source: Dissertations Abstracts International, Volume: 84-08, Section: B.

Thesis (Ph.D.)--University of Notre Dame, 2023.

Includes bibliographical references

Graph data analysis have recently attained much interests from the statistics community for their capabilities to perform inferential tasks on types of data that are prevailing at every corner of our daily life. Another hot topic is neural network which has been applied on various disciplines, like partial deferential equation(PDE), for their capabilities to deal with high dimensional problems that traditional finite elements or finite difference methods often fail to solve. My dissertation develops several methods that focus on various aspects across these two disciplines. In the graph-related realm, we firstly developed efficient numerical routines for unsupervised clustering problem and further proved theoretical guarantees on the clustering error corresponding to the numerical routines. For graph neural network, we modified the traditional training process of graph neural network by re-sampling the graph structure. To the best of our knowledge, we are the first to introduce the randomness into the training phase of graph neural network. On the PDE domain, we proposed structure-preserving neural-network-based numerical schemes to solve both L2-gradient flows and generalized diffusions. By using neural networks as tools for spatial discretization, we introduce a structure-preserving Eulerian algorithm to solve L2-gradient flows and a structure-preserving Lagrangian algorithm to solve generalized diffusions.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798368444437Subjects--Topical Terms:

1069907
Applied mathematics.
Subjects--Index Terms:

Partial deferential equationIndex Terms--Genre/Form:

554714
Electronic books.

Graph Related Data Analysis and Neural Network Based Partial Differential Equations Solver.
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100 1 $a Hu, Ziqing. $3 1466120
245 1 0 $a Graph Related Data Analysis and Neural Network Based Partial Differential Equations Solver.
264 0 $c 2023
300 $a 1 online resource (134 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
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500 $a Source: Dissertations Abstracts International, Volume: 84-08, Section: B.
500 $a Advisor: Xu, Zhiliang.
502 $a Thesis (Ph.D.)--University of Notre Dame, 2023.
504 $a Includes bibliographical references
520 $a Graph data analysis have recently attained much interests from the statistics community for their capabilities to perform inferential tasks on types of data that are prevailing at every corner of our daily life. Another hot topic is neural network which has been applied on various disciplines, like partial deferential equation(PDE), for their capabilities to deal with high dimensional problems that traditional finite elements or finite difference methods often fail to solve. My dissertation develops several methods that focus on various aspects across these two disciplines. In the graph-related realm, we firstly developed efficient numerical routines for unsupervised clustering problem and further proved theoretical guarantees on the clustering error corresponding to the numerical routines. For graph neural network, we modified the traditional training process of graph neural network by re-sampling the graph structure. To the best of our knowledge, we are the first to introduce the randomness into the training phase of graph neural network. On the PDE domain, we proposed structure-preserving neural-network-based numerical schemes to solve both L2-gradient flows and generalized diffusions. By using neural networks as tools for spatial discretization, we introduce a structure-preserving Eulerian algorithm to solve L2-gradient flows and a structure-preserving Lagrangian algorithm to solve generalized diffusions.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2024
538 $a Mode of access: World Wide Web
650 4 $a Applied mathematics. $3 1069907
650 4 $a Statistics. $3 556824
650 4 $a Computer science. $3 573171
653 $a Partial deferential equation
653 $a Graph-related realm
653 $a Efficient numerical routines
655 7 $a Electronic books. $2 local $3 554714
690 $a 0364
690 $a 0984
690 $a 0463
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a University of Notre Dame. $b Applied and Computational Mathematics and Statistics. $3 1466121
773 0 $t Dissertations Abstracts International $g 84-08B.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30000157 $z click for full text (PQDT)