A new variable shape parameter strategy for RBF approximation using neural networks

The choice of the shape parameter highly effects the behaviour of radial basis function (RBF) approximations, as it needs to be selected to balance between the ill-conditioning of the interpolation matrix and high accuracy. In this paper, we demonstrate how to use neural networks to determine the sh...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2023-08, Vol.143, p.151-168
Main Authors: Nassajian Mojarrad, Fatemeh, Han Veiga, Maria, Hesthaven, Jan S., Öffner, Philipp
Format: Article
Language:English
Subjects:
Artificial neural network
Meshfree methods
Radial basis function
Unsupervised learning
Variable shape parameter
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Summary:The choice of the shape parameter highly effects the behaviour of radial basis function (RBF) approximations, as it needs to be selected to balance between the ill-conditioning of the interpolation matrix and high accuracy. In this paper, we demonstrate how to use neural networks to determine the shape parameters in RBFs. In particular, we construct a multilayer perceptron (MLP) trained using an unsupervised learning strategy, and use it to predict shape parameters for inverse multiquadric and Gaussian kernels. We test the neural network approach in RBF interpolation tasks and in a RBF-finite difference method in one and two-space dimensions, demonstrating promising results.
ISSN:0898-1221
DOI:10.1016/j.camwa.2023.05.005