An Introduction to Neural Network Methods for Differential Equations (Paperback, 2015)

Preface. Introduction. 1 Overview of Differential Equation. 1.1 Classification of Differential Equations. 1.2 Types of Differential Equation Problems. 1.3 Differential Equations Associated with Physical Problems Arising in Engineering. 1.4 General Introduction of Numerical Methods for Solving Differential Equations. 1.5 Advantages of Neural Network Method for Solving Differential Equations. 2 History of Neural Networks. 2.1 The 1940's: The Beginning of Neural Nets. 2.2 The 1950's and 1960's: The First Golden Age of Neural Networks. 2.3 The 1970's: The Quiet Years. 2.4 The 1980's: Renewed Enthusiasm. 3 Preliminaries of Neural Networks. 3.1 What is Neural Network? 3.2 Biological Neural Network. 3.3 Artificial Neural Network. 3.4 Mathematical Model of Artificial Neural Network. 3.5 Activation Function. 3.6 Neural Network Architecture. 3.7 Learning in Neural Networks. 3.8 Multi-layer Perceptron. 3.9 Neural Networks as Universal Approximator. 4 Neural Network Methods for Solving Differential Equations. 4.1 Method of Multilayer Perceptron Neural Network. 4.2 Method of Radial Basis Function Neural Networks. 4.3 Method of Multiquadric Radial Basis Function Neural Network. 4.4 Method of Cellular Neural Networks. 4.5 Method of Finite Element Neural Networks. 4.6 Method of Wavelet Neural Networks. 4.7 Some Workout Examples. Conclusion. Appendix. References. Index.