國立虎尾科技大學 |

An Introduction to Neural Network Methods for Differential Equations

Record Type:	Language materials, printed : Monograph/item
Title/Author:	An Introduction to Neural Network Methods for Differential Equations/ by Neha Yadav, Anupam Yadav, Manoj Kumar.
Author:	Yadav, Neha.
other author:	Yadav, Anupam.
Description:	XIII, 114 p. 21 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Neural networks (Computer science) . -
Online resource:	https://doi.org/10.1007/978-94-017-9816-7
ISBN:	9789401798167

An Introduction to Neural Network Methods for Differential Equations
Yadav, Neha.

An Introduction to Neural Network Methods for Differential Equations[electronic resource] /by Neha Yadav, Anupam Yadav, Manoj Kumar. - 1st ed. 2015. - XIII, 114 p. 21 illus.online resource. - SpringerBriefs in Computational Intelligence,2625-3704. - SpringerBriefs in Computational Intelligence,.

Preface -- Introduction -- 1 Overview of Differential Equations -- 2 History of Neural Networks -- 3 Preliminaries of Neural Networks -- 4 Neural Network Methods for Solving Differential Equations -- Conclusion -- Appendix -- References -- Index.

This book introduces a variety of neural network methods for solving differential equations arising in science and engineering. The emphasis is placed on a deep understanding of the neural network techniques, which has been presented in a mostly heuristic and intuitive manner. This approach will enable the reader to understand the working, efficiency and shortcomings of each neural network technique for solving differential equations. The objective of this book is to provide the reader with a sound understanding of the foundations of neural networks, and a comprehensive introduction to neural network methods for solving differential equations together with recent developments in the techniques and their applications. The book comprises four major sections. Section I consists of a brief overview of differential equations and the relevant physical problems arising in science and engineering. Section II illustrates the history of neural networks starting from their beginnings in the 1940s through to the renewed interest of the 1980s. A general introduction to neural networks and learning technologies is presented in Section III. This section also includes the description of the multilayer perceptron and its learning methods. In Section IV, the different neural network methods for solving differential equations are introduced, including discussion of the most recent developments in the field. Advanced students and researchers in mathematics, computer science and various disciplines in science and engineering will find this book a valuable reference source.

ISBN: 9789401798167

Standard No.: 10.1007/978-94-017-9816-7doiSubjects--Topical Terms:

1253765
Neural networks (Computer science) .

LC Class. No.: QA76.87

Dewey Class. No.: 519

An Introduction to Neural Network Methods for Differential Equations
LDR:03188nam a22003975i 4500 001 969151
003 DE-He213
005 20200707014258.0
007 cr nn 008mamaa
008 201211s2015 ne | s |||| 0|eng d
020 $a 9789401798167 $9 978-94-017-9816-7
024 7 $a 10.1007/978-94-017-9816-7 $2 doi
035 $a 978-94-017-9816-7
050 4 $a QA76.87
072 7 $a PBWH $2 bicssc
072 7 $a MAT003000 $2 bisacsh
072 7 $a PBWH $2 thema
082 0 4 $a 519 $2 23
100 1 $a Yadav, Neha. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1066544
245 1 3 $a An Introduction to Neural Network Methods for Differential Equations $h [electronic resource] / $c by Neha Yadav, Anupam Yadav, Manoj Kumar.
250 $a 1st ed. 2015.
264 1 $a Dordrecht : $b Springer Netherlands : $b Imprint: Springer, $c 2015.
300 $a XIII, 114 p. 21 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a SpringerBriefs in Computational Intelligence, $x 2625-3704
505 0 $a Preface -- Introduction -- 1 Overview of Differential Equations -- 2 History of Neural Networks -- 3 Preliminaries of Neural Networks -- 4 Neural Network Methods for Solving Differential Equations -- Conclusion -- Appendix -- References -- Index.
520 $a This book introduces a variety of neural network methods for solving differential equations arising in science and engineering. The emphasis is placed on a deep understanding of the neural network techniques, which has been presented in a mostly heuristic and intuitive manner. This approach will enable the reader to understand the working, efficiency and shortcomings of each neural network technique for solving differential equations. The objective of this book is to provide the reader with a sound understanding of the foundations of neural networks, and a comprehensive introduction to neural network methods for solving differential equations together with recent developments in the techniques and their applications. The book comprises four major sections. Section I consists of a brief overview of differential equations and the relevant physical problems arising in science and engineering. Section II illustrates the history of neural networks starting from their beginnings in the 1940s through to the renewed interest of the 1980s. A general introduction to neural networks and learning technologies is presented in Section III. This section also includes the description of the multilayer perceptron and its learning methods. In Section IV, the different neural network methods for solving differential equations are introduced, including discussion of the most recent developments in the field. Advanced students and researchers in mathematics, computer science and various disciplines in science and engineering will find this book a valuable reference source.
650 0 $a Neural networks (Computer science) . $3 1253765
650 0 $a Differential equations. $3 527664
650 0 $a Physics. $3 564049
650 0 $a Applied mathematics. $3 1069907
650 0 $a Engineering mathematics. $3 562757
650 0 $a Computer mathematics. $3 1199796
650 1 4 $a Mathematical Models of Cognitive Processes and Neural Networks. $3 884110
650 2 4 $a Ordinary Differential Equations. $3 670854
650 2 4 $a Numerical and Computational Physics, Simulation. $3 1112293
650 2 4 $a Mathematical and Computational Engineering. $3 1139415
650 2 4 $a Computational Mathematics and Numerical Analysis. $3 669338
700 1 $a Yadav, Anupam. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1066545
700 1 $a Kumar, Manoj. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 786461
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9789401798174
776 0 8 $i Printed edition: $z 9789401798150
830 0 $a SpringerBriefs in Computational Intelligence, $x 2625-3704 $3 1254760
856 4 0 $u https://doi.org/10.1007/978-94-017-9816-7
912 $a ZDB-2-ENG
912 $a ZDB-2-SXE
950 $a Engineering (SpringerNature-11647)
950 $a Engineering (R0) (SpringerNature-43712)