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

Record Type:	Electronic resources : Monograph/item
Title/Author:	Graph Related Data Analysis and Neural Network Based Partial Differential Equations Solver.
Author:	Hu, Ziqing.
Published:	Ann Arbor : ProQuest Dissertations & Theses, 2023
Description:	134 p.
Notes:	Source: Dissertations Abstracts International, Volume: 84-08, Section: B.
Notes:	Advisor: Xu, Zhiliang.
Contained By:	Dissertations Abstracts International84-08B.
Subject:	Applied mathematics.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30000157
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. - Ann Arbor : ProQuest Dissertations & Theses, 2023 - 134 p.

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

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

This item must not be sold to any third party vendors.

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.

ISBN: 9798368444437Subjects--Topical Terms:

377601
Applied mathematics.
Subjects--Index Terms:

Partial deferential equation

Graph Related Data Analysis and Neural Network Based Partial Differential Equations Solver.
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100 1 $a Hu, Ziqing. $3 966783
245 1 0 $a Graph Related Data Analysis and Neural Network Based Partial Differential Equations Solver.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2023
300 $a 134 p.
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.
506 $a This item must not be sold to any third party vendors.
506 $a This item must not be added to any third party search indexes.
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.
590 $a School code: 0165.
650 4 $a Applied mathematics. $3 377601
650 4 $a Statistics. $3 182057
650 4 $a Computer science. $3 199325
653 $a Partial deferential equation
653 $a Graph-related realm
653 $a Efficient numerical routines
690 $a 0364
690 $a 0984
690 $a 0463
710 2 $a University of Notre Dame. $b Applied and Computational Mathematics and Statistics. $3 942418
773 0 $t Dissertations Abstracts International $g 84-08B.
790 $a 0165
791 $a Ph.D.
792 $a 2023
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30000157