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Introduction to Neural Network Methods for Differential Equations 2015 ed. [Pehme köide]

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  • Formaat: Paperback / softback, 114 pages, kõrgus x laius: 235x155 mm, kaal: 2058 g, 21 Illustrations, black and white; XIII, 114 p. 21 illus., 1 Paperback / softback
  • Sari: SpringerBriefs in Computational Intelligence
  • Ilmumisaeg: 23-Mar-2015
  • Kirjastus: Springer
  • ISBN-10: 940179815X
  • ISBN-13: 9789401798150
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Introduction to Neural Network Methods for Differential Equations 2015 ed.Suurem pilt
  • Formaat: Paperback / softback, 114 pages, kõrgus x laius: 235x155 mm, kaal: 2058 g, 21 Illustrations, black and white; XIII, 114 p. 21 illus., 1 Paperback / softback
  • Sari: SpringerBriefs in Computational Intelligence
  • Ilmumisaeg: 23-Mar-2015
  • Kirjastus: Springer
  • ISBN-10: 940179815X
  • ISBN-13: 9789401798150
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9789401798150.html
Märksõnad:
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.

Arvustused

The book is intended to enable the reader to get an image on the variety of NN and the NN methods can be used in solving differential equations. It is a valuable reference material both from the presentation point of view and the provided references. (Liviu Gora, zbMATH 1328.92006, 2016)

1 Overview of Differential Equations
1(12)
1.1 Classification of Differential Equations
1(2)
1.1.1 Ordinary Differential Equations
1(1)
1.1.2 Partial Differential Equations
2(1)
1.1.3 Delay Differential Equations
2(1)
1.1.4 Stochastic Differential Equations
2(1)
1.1.5 Differential Algebraic Equations
3(1)
1.2 Types of Differential Equation Problems
3(2)
1.2.1 Initial Value Problem
3(1)
1.2.2 Boundary Value Problem
3(2)
1.3 Differential Equations Associated with Physical Problems Arising in Engineering
5(1)
1.4 General Introduction of Numerical Methods for Solving Differential Equations
5(6)
1.4.1 Shooting Method
6(1)
1.4.2 Finite Difference Method
6(2)
1.4.3 Finite Element Method
8(1)
1.4.4 Finite Volume Method
9(1)
1.4.5 Spline Based Method
9(2)
1.4.6 Neural Network Method
11(1)
1.5 Advantages of Neural Network Method for Solving Differential Equations
11(2)
2 History of Neural Networks
13(4)
2.1 The 1940s: The Beginning of Neural Networks
13(1)
2.2 The 1950s and 1960s: The First Golden Age of Neural Networks
14(1)
2.3 The 1970s: The Quiet Years
15(1)
2.4 The 1980s: Renewed Enthusiasm
15(2)
3 Preliminaries of Neural Networks
17(26)
3.1 What Is Neural Network?
17(1)
3.2 Biological Neural Network
18(1)
3.3 Artificial Neural Network
19(1)
3.4 Mathematical Model of Artificial Neural Network
19(2)
3.5 Activation Function
21(3)
3.5.1 Linear Activation Function
22(1)
3.5.2 Sign Activation Function
22(1)
3.5.3 Sigmoid Activation Function
22(1)
3.5.4 Step Activation Function
23(1)
3.6 Neural Network Architecture
24(9)
3.6.1 Feed Forward Neural Networks
24(1)
3.6.2 Recurrent Neural Networks
25(1)
3.6.3 Radial Basis Function Neural Network
26(2)
3.6.4 Hopfield Network
28(2)
3.6.5 Cellular Neural Network
30(1)
3.6.6 Finite Element Neural Network
31(1)
3.6.7 Wavelet Neural Network
31(2)
3.7 Learning in Neural Networks
33(1)
3.7.1 Supervised Learning
33(1)
3.7.2 Unsupervised Learning
34(1)
3.7.3 Reinforcement Learning
34(1)
3.7.4 Competitive Learning
34(1)
3.8 Multi-layer Perceptron
34(7)
3.8.1 Backpropagation Algorithm
35(1)
3.8.2 The RPROP Learning Algorithm
35(2)
3.8.3 The Levenberg-Marquardt Learning Algorithm
37(1)
3.8.4 Genetic Algorithm
38(2)
3.8.5 Particle Swarm Optimization
40(1)
3.9 Neural Networks as Universal Approximator
41(2)
4 Neural Network Methods for Solving Differential Equations
43(58)
4.1 Method of Multilayer Perceptron Neural Network
43(22)
4.1.1 Gradient Computation
44(1)
4.1.2 Gradient Computation with Respect to Network Inputs
45(1)
4.1.3 Gradient Computation with Respect to Network Parameters
46(1)
4.1.4 Network Parameter Updation
46(1)
4.1.5 Recent Development in MLPNN for Solving Differential Equations
47(18)
4.2 Method of Radial Basis Function Neural Networks
65(2)
4.3 Method of Multiquadric Radial Basis Function Neural Network
67(10)
4.3.1 DRBFN Procedure for Solving Differential Equations
67(2)
4.3.2 IRBFN Procedure for Solving Differential Equations
69(1)
4.3.3 Recent Development in the RBF and MQRBF Neural Network Techniques
69(8)
4.4 Method of Cellular Neural Networks
77(11)
4.4.1 Principle for CNN Templates Findings
78(2)
4.4.2 Design of the Complete CNN Processor
80(1)
4.4.3 Recent Development in the Cellular Neural Network Technique
80(8)
4.5 Method of Finite Element Neural Networks
88(3)
4.5.1 Boundary Conditions in FENN
90(1)
4.6 Method of Wavelet Neural Networks
91(2)
4.7 Some Workout Examples
93(8)
Conclusion 101(2)
Appendix 103(2)
References 105(6)
Index 111
Dr. Neha Yadav, Assistant Professor (Mathematics), Department of Applied Science, ITM University Gurgaon, Haryana-122017, India. Specialization: Numerical Analysis and Soft Computing Techniques, Differential Equations, Boundary Value Problems. Total Experience: 03 Years Teaching and 04 years Research Experience. Research Papers in Refereed SCI journals : 03 (Published), 03 (Submitted). Awards and Prizes: (i) Travel Award from CSIR-HRDG and NBHM (Govt. of India) to visit University of Strathclyde, Glasgow, U.K. in the year 2013. (ii) Qualified UGC-NET JRF in the year 2010. (iii) Selected for half financial to participate in School and Conference on Computation Methods in Dynamics at Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, from 20 June to 8 July 2011. (iv) Selected for MHRD Institute Fellowship in PhD at MNNIT Allahabad. (v) Selected for Summer Research Fellowship Programme jointly sponsored by IASc (Bangalore), INSA(New Delhi) and NASI(Allahabad).





Dr. Anupam Yadav, Assistant Professor (Mathematics). National Institute of Technology Uttarakhand. Pauri Garhwal, Uttarakhand - 246174. Specialization: Soft Computing Techniques, Swarm Intelligence, Artificial Intelligence. Area of Research: Optimization, Operations Research. Research Papers in Refereed SCI journals : 04 (Published), 04 (Submitted). Awards: Award from NBHM-DAE (Govt. of India) to visit Glasgow, U. K. in the year 2013. Award from CSIR-HRDG (Govt. Of India) to visit Taipei, Taiwan in the year 2011. CSIR JRF (Mathematical Sciences) in the year 2009. GATE 2009 with All India Rank 95. Positions held: Asst. Professor National Institute of Technology Uttarakhand, India. Research Professor: DPST Center, Korea University, Seoul, South Korea. Senior Research Fellow: IIT Roorkee, India. Junior Research Fellow: IIT Roorkee, India.

Dr. Manoj Kumar, Associate Professor (Mathematics), Motilal Nehru National Institute of Technology, Allahabad, India-211004. Specializations: Numerical Analysis and Computer Application, Simulation & Modeling. Area of Research: Numerical Analysis/Operation Research/Mathematical Modeling/Partial Differential Equations/ Computational Fluid Dynamics. Teaching Experience : Since 2001 teaching B.Tech, M.Tech, MCA classes and guiding PhD/ Post-Doctoral Students. Research Papers in Refereed SCI Journals:  67. PhD Student Guided: 09 (Awarded) , 02(Work in Progress). Post-Doctoral Guidance:04. Independent Research Grants: 04. Reviewer of International Journals: 11.