Regression-based neural network training for the solution of ordinary differential equations. (1st January 2013)

• Record Type: Journal Article
• Authors: Mall, Susmita; Chakraverty, S.
• Is Part Of: International journal of mathematical modelling and numerical optimisation. Volume 4:Number 2(2013)
• Page Start: 136
• Page End: 149
• Publication Date: 2013-01-01
• Subjects: ordinary differential equation -- ODE -- feed forward neural network -- unsupervised algorithm -- back propagation -- regression; Mathematical models -- Periodicals; Mathematical optimization -- Periodicals; 519.605
• Languages: English
• ISSNs: 2040-3607

Abstract

In this paper, we have introduced a method which is based on the use of unsupervised type of regression-based algorithm (RBA) for solving ordinary differential equations (ODEs) with initial or boundary conditions. Approximate solution of differential equation is differentiable and closed analytic. Here we have used error back propagation method for minimising the error function and modification of the parameters without direct use of other optimisation techniques. Initial weights are taken as combination of random as well as by proposed regression-based method. We present the method for solving a variety of problems and the results with arbitrary and regression-based initial weights are compared. Here the number of nodes in hidden layer has been fixed according to the degree of polynomial in the regression. The present model demonstrates to get also the approximate solutions for the differential equation inside and outside of the training domain.