04874nam 22008175 450 991029967680332120251113185139.094-017-9816-810.1007/978-94-017-9816-7(CKB)3710000000360463(EBL)1998188(OCoLC)904248956(SSID)ssj0001452104(PQKBManifestationID)11890637(PQKBTitleCode)TC0001452104(PQKBWorkID)11479644(PQKB)10407921(DE-He213)978-94-017-9816-7(MiAaPQ)EBC1998188(PPN)184495423(EXLCZ)99371000000036046320150226d2015 u| 0engur|n|---|||||txtccrAn Introduction to Neural Network Methods for Differential Equations /by Neha Yadav, Anupam Yadav, Manoj Kumar1st ed. 2015.Dordrecht :Springer Netherlands :Imprint: Springer,2015.1 online resource (124 p.)SpringerBriefs in Computational Intelligence,2625-3712Description based upon print version of record.94-017-9815-X Includes bibliographical references and index.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 beginningsin 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.SpringerBriefs in Computational Intelligence,2625-3712Neural networks (Computer science)Differential equationsMathematical physicsEngineering mathematicsEngineeringData processingMathematicsData processingMathematical Models of Cognitive Processes and Neural NetworksDifferential EquationsTheoretical, Mathematical and Computational PhysicsMathematical and Computational Engineering ApplicationsComputational Mathematics and Numerical AnalysisNeural networks (Computer science)Differential equations.Mathematical physics.Engineering mathematics.EngineeringData processing.MathematicsData processing.Mathematical Models of Cognitive Processes and Neural Networks.Differential Equations.Theoretical, Mathematical and Computational Physics.Mathematical and Computational Engineering Applications.Computational Mathematics and Numerical Analysis.006.32Yadav Nehaauthttp://id.loc.gov/vocabulary/relators/aut720897Yadav Anupamauthttp://id.loc.gov/vocabulary/relators/autKumar Manojauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910299676803321An Introduction to Neural Network Methods for Differential Equations2497650UNINA