Regression-based neural network training for the solution of ordinary differential equations Online publication date: Sat, 26-Jul-2014
by Susmita Mall; S. Chakraverty
International Journal of Mathematical Modelling and Numerical Optimisation (IJMMNO), Vol. 4, No. 2, 2013
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.
Existing subscribers:
Go to Inderscience Online Journals to access the Full Text of this article.
If you are not a subscriber and you just want to read the full contents of this article, buy online access here.Complimentary Subscribers, Editors or Members of the Editorial Board of the International Journal of Mathematical Modelling and Numerical Optimisation (IJMMNO):
Login with your Inderscience username and password:
Want to subscribe?
A subscription gives you complete access to all articles in the current issue, as well as to all articles in the previous three years (where applicable). See our Orders page to subscribe.
If you still need assistance, please email subs@inderscience.com
Our Blog 
Follow us on Twitter 
Visit us on Facebook