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Neural Computing and Applications

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01-09-2014 | Original Article

Regression-based weight generation algorithm in neural network for solution of initial and boundary value problems

Authors: S. Chakraverty, Susmita Mall

Published in: Neural Computing and Applications | Issue 3-4/2014

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Abstract

This paper introduces a new algorithm for solving ordinary differential equations (ODEs) with initial or boundary conditions. In our proposed method, the trial solution of differential equation has been used in the regression-based neural network (RBNN) model for single input and single output system. The artificial neural network (ANN) trial solution of ODE is written as sum of two terms, first one satisfies initial/boundary conditions and contains no adjustable parameters. The second part involves a RBNN model containing adjustable parameters. Network has been trained using the initial weights generated by the coefficients of regression fitting. We have used feed-forward neural network and error back propagation algorithm for minimizing error function. Proposed model has been tested for first, second and fourth-order ODEs. We also compare the results of proposed algorithm with the traditional ANN algorithm. The idea may very well be extended to other complicated differential equations.

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Title: Regression-based weight generation algorithm in neural network for solution of initial and boundary value problems
Authors: S. Chakraverty
Susmita Mall
Publication date: 01-09-2014
Publisher: Springer London
Published in: Neural Computing and Applications / Issue 3-4/2014
Print ISSN: 0941-0643
Electronic ISSN: 1433-3058
DOI: https://doi.org/10.1007/s00521-013-1526-4

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