Solving ordinary differential equations using wavelet neural networks

In this paper, we present an artificial neural network (ANN) approach to approximate the solutions of ordinary differential equations (ODEs) with initial conditions. The wavelet neural networks (WNNs) with Gaussian wavelet and Mexican Hat activation functions are applied as universal approximators....

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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
Boundary value problems
Differential equations
Error functions
Initial conditions
Momentum
Neural networks
Numerical methods
Optimization
Ordinary differential equations
Wavelet analysis
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Summary:In this paper, we present an artificial neural network (ANN) approach to approximate the solutions of ordinary differential equations (ODEs) with initial conditions. The wavelet neural networks (WNNs) with Gaussian wavelet and Mexican Hat activation functions are applied as universal approximators. The proposed methods convert the application of solving ODEs from a constrained optimization problem into an unconstrained optimization problem by satisfying the initial conditions exactly. Then, the momentum backpropagation (mBP) is employed to minimize the unsupervised error function, in which the only adjustable parameters are the weights from the hidden layer to the output layer. Initial value problems (IVPs) are solved to illustrate the applicability and accuracy of the proposed momentum backpropagation wavelet neural network (mBPWNN) methods. In comparison with the solutions of other existing ANN methods, numerical results showed that the mBPWNN methods yield a superior accuracy.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.5136487