Solving ordinary differential equations using neural networks

This paper presents artificial neural networks (ANNs) for solving ordinary differential equations (ODEs) with modified back propagation (mBP). The multilayer perceptron neural networks (MPNNs) are chosen as ANNs model which have universal approximation power that is beneficial in solving ODEs. This...

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Bibliographic Details
Main Authors: Tan, Lee Sen, Zainuddin, Zarita, Ong, Pauline
Format: Conference Proceeding
Language:English
Subjects:
Approximation
Artificial neural networks
Back propagation networks
Boundary value problems
Computer simulation
Differential equations
Multilayer perceptrons
Neural networks
Ordinary differential equations
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Summary:This paper presents artificial neural networks (ANNs) for solving ordinary differential equations (ODEs) with modified back propagation (mBP). The multilayer perceptron neural networks (MPNNs) are chosen as ANNs model which have universal approximation power that is beneficial in solving ODEs. This mBP training algorithm which has additional momentum is employed to update the network parameters in the way of unsupervised training. The developed method is applied to solve initial value problems (IVPs) and boundary value problems (BVPs) of ODEs. Simulation results of MPNNs are compared with analytic solutions to show that solutions of ODEs with high accuracy of approximation and fast convergence are obtained by means of ANNs.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.5041601