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 ill-condition of the interpolation matrix and high accuracy. In this paper, we demonstrate how to use neural networks to determine the shape par...

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Bibliographic Details
Published in:arXiv.org 2024-06
Main Authors: Mojarrad, Fatemeh Nassajian, Maria Han Veiga, Hesthaven, Jan S, Öffner, Philipp
Format: Article
Language:English
Subjects:
Approximation
Finite difference method
Interpolation
Multilayer perceptrons
Neural networks
Parameters
Radial basis function
Shape effects
Online Access:Get full text
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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 ill-condition 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 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:2331-8422
DOI:10.48550/arxiv.2210.16945