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Nonlinear Computations in Neural Networks and Applications.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Nonlinear Computations in Neural Networks and Applications./
Author:	Chen, Qipin.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2020,
Description:	132 p.
Notes:	Source: Dissertations Abstracts International, Volume: 83-03, Section: B.
Contained By:	Dissertations Abstracts International83-03B.
Subject:	Deep learning. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28767679
ISBN:	9798535589176

Nonlinear Computations in Neural Networks and Applications.
Chen, Qipin.

Nonlinear Computations in Neural Networks and Applications. - Ann Arbor : ProQuest Dissertations & Theses, 2020 - 132 p.

Source: Dissertations Abstracts International, Volume: 83-03, Section: B.

Thesis (Ph.D.)--The Pennsylvania State University, 2020.

This thesis is devoted to provide some algorithms of nonlinear scientific computation based on deep neural networks. In the first chapter, we briefly introduce the concept and different applications of deep neural network, as well as some problems arising from different fields of computing. In the second chapter, we present a Homotopy Training Algorithm (HTA) to solve optimization problems arising from fully connected neural networks with complicated structures. The HTA dynamically builds the neural network starting from a simplified version and ending with the fully connected network via adding layers and nodes adaptively. In the third chapter, we develop a more general homotopy training algorithm to solve optimization problems arising from fully connected neural networks. By constructing a homotopy from a linear activation function to the ReLU function, we track the solution path from the linear regression solution to a good minimum of neural networks. In the fourth chapter, we develop a randomized Newton's method for solving differential equations, based on a fully connected neural network discretization. In particular, the randomized Newton's method randomly chooses equations from the overdetermined nonlinear system resulting from the neural network discretization and solves the nonlinear system adaptively. In the fifth chapter, we propose a novel weight initialization strategy that is based on the linear product structure (LPS) of neural networks. The proposed strategy is derived from the polynomial approximation of activation functions by using theories of numerical algebraic geometry to guarantee to find all the local minima. In the last chapter, we propose a one dimensional convolutional neural network - PWVNet to predict cardiovascular diseases (CVDs) from the arterial pressure waveform. After training the network on dataset generated from Kailuan Study, PWVNet outperforms the traditional method on CVD prediction by increasing the mean AUC by 0.266 on three validation datasets.

ISBN: 9798535589176Subjects--Topical Terms:

3554982
Deep learning.
Subjects--Index Terms:

Nonlinear scientific computation

Nonlinear Computations in Neural Networks and Applications.
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245 1 0 $a Nonlinear Computations in Neural Networks and Applications.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2020
300 $a 132 p.
500 $a Source: Dissertations Abstracts International, Volume: 83-03, Section: B.
500 $a Advisor: Hao, Wenrui.
502 $a Thesis (Ph.D.)--The Pennsylvania State University, 2020.
520 $a This thesis is devoted to provide some algorithms of nonlinear scientific computation based on deep neural networks. In the first chapter, we briefly introduce the concept and different applications of deep neural network, as well as some problems arising from different fields of computing. In the second chapter, we present a Homotopy Training Algorithm (HTA) to solve optimization problems arising from fully connected neural networks with complicated structures. The HTA dynamically builds the neural network starting from a simplified version and ending with the fully connected network via adding layers and nodes adaptively. In the third chapter, we develop a more general homotopy training algorithm to solve optimization problems arising from fully connected neural networks. By constructing a homotopy from a linear activation function to the ReLU function, we track the solution path from the linear regression solution to a good minimum of neural networks. In the fourth chapter, we develop a randomized Newton's method for solving differential equations, based on a fully connected neural network discretization. In particular, the randomized Newton's method randomly chooses equations from the overdetermined nonlinear system resulting from the neural network discretization and solves the nonlinear system adaptively. In the fifth chapter, we propose a novel weight initialization strategy that is based on the linear product structure (LPS) of neural networks. The proposed strategy is derived from the polynomial approximation of activation functions by using theories of numerical algebraic geometry to guarantee to find all the local minima. In the last chapter, we propose a one dimensional convolutional neural network - PWVNet to predict cardiovascular diseases (CVDs) from the arterial pressure waveform. After training the network on dataset generated from Kailuan Study, PWVNet outperforms the traditional method on CVD prediction by increasing the mean AUC by 0.266 on three validation datasets.
590 $a School code: 0176.
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650 4 $a Partial differential equations. $3 2180177
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650 4 $a Optimization. $3 891104
650 4 $a Neural networks. $3 677449
650 4 $a Classification. $3 595585
650 4 $a Cardiovascular disease. $3 3564561
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650 4 $a Algorithms. $3 536374
650 4 $a Error analysis. $3 3562845
650 4 $a Efficiency. $3 753744
650 4 $a Parameter estimation. $3 567557
650 4 $a Computer science. $3 523869
650 4 $a Bioinformatics. $3 553671
650 4 $a Artificial intelligence. $3 516317
653 $a Nonlinear scientific computation
653 $a Homotopy training
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653 $a Differential equations
653 $a Newton's method
653 $a Weight initialization
653 $a One dimensional convolutional neural network
653 $a Predicting cardiovascular disease
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