How Machine Learning is Innovating Today's World

18Alternate Approach to Solve Differential Equations Using Artificial Neural Network with Optimization Technique

Ramanan R.¹, Sukanta Nayak^2* and Arun Kumar Gupta³

¹Cognizant Technology Solution, Coimbatore, India

²Department of Mathematics, School of Advanced Sciences, VIT-AP University, Amaravati, Andhra Pradesh, India

³Department of Mathematics, School of Applied Sciences, KIIT Deemed to be University, Bhubaneswar, Odisha, India

Abstract

Differential equations are an essential part of mathematical modeling for various engineering and science problems. In this regard, many systems are data driven and hence the modeled differential equation too. In this context, the Artificial Neural Network (ANN) is a well-known model inspired by the Natural Neural Network (NNN) to simulate, analyze, and process the information. It possesses three layers, viz., input, hidden, and output, by which one can process the information at hand. As such, this chapter includes the idea of ANN with the steepest descent search optimization technique to solve ordinary differential equations and a system identification structural problem. The backpropagation technique has also been adopted to solve the aforementioned problems and to compare the acquired results. Both methods are found to be effective for solving ODEs by constructing the appropriate form of trial solutions. The obtained results clearly manifest that this neural network architecture with optimization technique is simple, efficient, and ...