Artificial Neural Networks for Engineers and Scientists

Dr. S. Chakraverty has over 25 years of experience as a researcher and teacher. Currently, he is working at the National Institute of Technology, Rourkela, Odisha as a full Professor and Head of the Department of Mathematics. Prior to this, he was with CSIRCentral Building Research Institute, Roorkee, India. After graduating from St. Columba’s College (Ranchi University), he obtained his M. Sc in Mathematics and M. Phil in Computer Applications from the University of Roorkee (now the Indian Institute of Technology Roorkee), earning First Position in the University honors. Dr. Chakraverty received his Ph. D. from IIT Roorkee in 1992. Afterwards, he did his post-doctoral research at Institute of Sound and Vibration Research (ISVR), University of Southampton, U.K. and at the Faculty of Engineering and Computer Science, Concordia University, Canada. He was also a visiting professor at Concordia and McGill Universities, Canada, during 1997-1999 and visiting professor of University of Johannesburg, South Africa during 2011-2014.Mrs. Susmita Mall received her M. Sc. degree in Mathematics from Ravenshaw University, Cuttack, Odisha, India in 2003. Currently she is a Senior Research Fellow in National Institute of Technology, Rourkela - 769 008, Odisha, India. She has been awarded Women Scientist Scheme-A (WOS-A) fellowship, under Department of Science and Technology (DST), Government of India to undertake her Ph. D. studies. Her current research interest includes Mathematical Modeling, Artificial Neural Network, Differential equations and Numerical analysis. To date, she has published seven research papers in international refereed journals and five in conferences.

• 1. Preliminaries of Artificial Neural Network1.1 Introduction1.2 Architecture of ANN1.2.1 Feed-Forward Neural Network1.2.2 Feedback Neural Network1.3 Paradigms of Learning1.3.1 Supervised Learning or Associative Learning1.3.2 Unsupervised or Self-Organization Learning1.4 Learning Rules or Learning Processes1.4.1 Error Back-Propagation Learning Algorithm or DeltaLearning Rule1.5 Activation Functions1.5.1 Sigmoid Function1.5.1.1 Unipolar Sigmoid Function1.5.1.2 Bipolar Sigmoid Function1.5.2 Tangent Hyperbolic FunctionReferences2. Preliminaries of Ordinary Differential Equations2.1 Definitions2.1.1 Order and Degree of DEs2.1.2 Ordinary Differential Equation2.1.3 Partial Differential Equation2.1.4 Linear and Nonlinear Differential Equations2.1.5 Initial Value Problem2.1.6 Boundary Value ProblemReferences3. Multilayer Artificial Neural Network3.1 Structure of Multilayer ANN Model3.2 Formulations and Learning Algorithm of MultilayerANN Model3.2.1 General Formulation of ODEs Based on ANN Model3.2.2 Formulation of nth-Order IVPs3.2.2.1 Formulation of First-Order IVPs3.2.2.2 Formulation of Second-Order IVPs3.2.3 Formulation of BVPs3.2.3.1 Formulation of Second-Order BVPs3.2.3.2 Formulation of Fourth-Order BVPs3.2.4 Formulation of a System of First-Order ODEs3.2.5 Computation of Gradient of ODEs for MultilayerANN Model3.3 First-Order Linear ODEs3.4 Higher-Order ODEs3.5 System of ODEsReferences4. Regression-Based ANN4.1 Algorithm of RBNN Model4.2 Structure of RBNN Model4.3 Formulation and Learning Algorithm of RBNN Model4.4 Computation of Gradient for RBNN Model4.5 First-Order Linear ODEs4.6 Higher-Order Linear ODEsReferences5. Single-Layer Functional Link Artificial Neural Network5.1 Single-Layer FLANN Models5.1.1 ChNN Model5.1.1.1 Structure of the ChNN Model5.1.1.2 Formulation of the ChNN Model5.1.1.3 Gradient Computation of the ChNN Model5.1.2 LeNN Model5.1.2.1 Structure of the LeNN Model5.1.2.2 Formulation of the LeNN Model5.1.2.3 Gradient Computation of the LeNN Model5.1.3 HeNN Model5.1.3.1 Architecture of the HeNN Model5.1.3.2 Formulation of the HeNN Model5.1.4 Simple Orthogonal Polynomial–Based NeuralNetwork (SOPNN) Model5.1.4.1 Structure of the SOPNN Model5.1.4.2 Formulation of the SOPNN Model5.1.4.3 Gradient Computation of the SOPNN Model5.2 First-Order Linear ODEs5.3 Higher-Order ODEs5.4 System of ODEsReferences6. Single-Layer Functional Link Artificial Neural Networkwith Regression-Based Weights6.1 ChNN Model with Regression-Based Weights6.1.1 Structure of the ChNN Model6.1.2 Formulation and Gradient Computationof the ChNN Model6.2 First-Order Linear ODEs6.3 Higher-Order ODEsReferences7. Lane–Emden Equations7.1 Multilayer ANN-Based Solution of Lane–Emden Equations7.2 FLANN-Based Solution of Lane–Emden Equations7.2.1 Homogeneous Lane–Emden Equations7.2.2 Nonhomogeneous Lane–Emden EquationReferences8. Emden–Fowler Equations8.1 Multilayer ANN-Based Solution of Emden–FowlerEquations8.2 FLANN-Based Solution of Emden–Fowler EquationsReferences9. Duffing Oscillator Equations9.1 Governing Equation9.2 Unforced Duffing Oscillator Equations9.3 Forced Duffing Oscillator EquationsReferences10. Van der Pol–Duffing Oscillator Equation10.1 Model Equation10.2 Unforced Van der Pol–Duffing Oscillator Equation10.3 Forced Van der Pol–Duffing Oscillator EquationReferences