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

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 syste...

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Vydáno v:Neural computing & applications Ročník 25; číslo 3-4; s. 585 - 594
Hlavní autoři: Chakraverty, S., Mall, Susmita
Médium: Journal Article
Jazyk:angličtina
Vydáno: London Springer London 01.09.2014
Springer
Témata:
Applied sciences
Artificial Intelligence
Computational Biology/Bioinformatics
Computational Science and Engineering
Computer Science
Computer science; control theory; systems
Connectionism. Neural networks
Data Mining and Knowledge Discovery
Exact sciences and technology
Image Processing and Computer Vision
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Original Article
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Probability and Statistics in Computer Science
Sciences and techniques of general use
Feed-forward model
Error back propagation
Regression fitting
Artificial neural network
Differential equation
Backpropagation
Input output
Initial condition
Initial value problem
Error function
Minimization
Regression analysis
Neural network
Boundary condition
Modeling
Weighted graph
Backpropagation algorithm
First order equation
Boundary value problem
Feedforward neural nets
Regression model
Feedforward
Growth of error
Mathematical programming
ISSN:0941-0643, 1433-3058
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Popis
Shrnutí: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.
ISSN:0941-0643
1433-3058
DOI:10.1007/s00521-013-1526-4