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Deep Learning Methods for Some Problems in Scientific Computing /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Deep Learning Methods for Some Problems in Scientific Computing /Yuankai Teng.
Author:	Teng, Yuankai,
Description:	1 electronic resource (101 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-04, Section: B.
Notes:	Advisors: Ju, Lili; Wang, Zhu Committee members: Sun, Yi; Liu, Xinfeng; Wang, Yi.
Contained By:	Dissertations Abstracts International85-04B.
Subject:	Mathematics.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30417268
ISBN:	9798380436472

Deep Learning Methods for Some Problems in Scientific Computing /
Teng, Yuankai,

Deep Learning Methods for Some Problems in Scientific Computing /Yuankai Teng. - 1 electronic resource (101 pages)

Source: Dissertations Abstracts International, Volume: 85-04, Section: B.

Deep learning has emerged as a powerful approach for solving complex problems in scientific computing due to the increasing availability of large-scale data and computational resources. This thesis explores the potential of deep learning methods for three specific problems in scientific computing: (i) reducing the dimensions of variables in function approximation, (ii) solving linear reaction-diffusion equations, and (iii) finding the parametric representations of parameters in the numerical schemes for solving time-dependent partial differential equations.For the first problem, a novel deep learning architecture is developed for reducing the dimensions of variables in function approximation. The proposed method achieves state-of-the-art performance on given testing examples and real-world related problems. For the second problem, a deep learning-based method using a fully connected network structure is proposed for solving linear reaction-diffusion equations. The proposed method outperforms existing numerical methods on benchmark problems. For the third problem, a deep learning framework using convolutional neural networks is developed for finding parametric representations of parameters in numerical schemes for solving time-dependent PDEs. The proposed method is shown to be effective on various problems.The contributions of this thesis have significant implications for advancing the state-of-the-art in scientific computing, enabling more accurate and efficient solutions to complex problems in science and engineering. The proposed deep learning methods provide a promising alternative to existing numerical methods for solving the considered problems and have the potential to greatly accelerate scientific discovery and innovation.

English

ISBN: 9798380436472Subjects--Topical Terms:

184409
Mathematics.
Subjects--Index Terms:

Scientific computing

Deep Learning Methods for Some Problems in Scientific Computing /
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520 $a Deep learning has emerged as a powerful approach for solving complex problems in scientific computing due to the increasing availability of large-scale data and computational resources. This thesis explores the potential of deep learning methods for three specific problems in scientific computing: (i) reducing the dimensions of variables in function approximation, (ii) solving linear reaction-diffusion equations, and (iii) finding the parametric representations of parameters in the numerical schemes for solving time-dependent partial differential equations.For the first problem, a novel deep learning architecture is developed for reducing the dimensions of variables in function approximation. The proposed method achieves state-of-the-art performance on given testing examples and real-world related problems. For the second problem, a deep learning-based method using a fully connected network structure is proposed for solving linear reaction-diffusion equations. The proposed method outperforms existing numerical methods on benchmark problems. For the third problem, a deep learning framework using convolutional neural networks is developed for finding parametric representations of parameters in numerical schemes for solving time-dependent PDEs. The proposed method is shown to be effective on various problems.The contributions of this thesis have significant implications for advancing the state-of-the-art in scientific computing, enabling more accurate and efficient solutions to complex problems in science and engineering. The proposed deep learning methods provide a promising alternative to existing numerical methods for solving the considered problems and have the potential to greatly accelerate scientific discovery and innovation.
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