Mathematical Methods in Interdisciplinary Sciences

1Connectionist Learning Models for Application Problems Involving Differential and Integral Equations

Susmita Mall, Sumit Kumar Jeswal, and Snehashish Chakraverty

Department of Mathematics, National Institute of Technology Rourkela, Rourkela, Odisha, 769008, India

1.1 Introduction

1.1.1 Artificial Neural Network

Artificial intelligence (AI) also coined as machine intelligence is the concept and development of intelligent machines that work and react like humans. In the twentieth century, AI has a great impact starting from human life to various industries. Researchers from various parts of the world are developing new methodologies based on AI so as to make human life more comfortable. AI has different research areas such as artificial neural network (ANN), genetic algorithm (GA), support vector machine (SVM), fuzzy concept, etc.

In 1943, McCulloh and Pitts [1] designed a computational model for neural network based on mathematical concepts. The concept of perceptron has been proposed by Rosenblatt [2]. In the year 1975, Werbos [3] introduced the well‐known concept of backpropagation algorithm. After the creation of backpropagation algorithm, different researchers explored the various aspects of neural network.

The concept of ANN inspires from the biological neural systems. Neural network consists of a number of identical units known as artificial neurons. Mainly, neural network comprises three layers, viz., input, hidden, and output. Each neuron in the nth layer has been ...