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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2210.16945 |
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| _version_ | 1866917703922483200 |
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| author | Mojarrad, Fatemeh Nassajian Veiga, Maria Han Hesthaven, Jan S. Öffner, Philipp |
| author_facet | Mojarrad, Fatemeh Nassajian Veiga, Maria Han Hesthaven, Jan S. Öffner, Philipp |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_16945 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A new variable shape parameter strategy for RBF approximation using neural networks Mojarrad, Fatemeh Nassajian Veiga, Maria Han Hesthaven, Jan S. Öffner, Philipp Numerical Analysis 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. |
| title | A new variable shape parameter strategy for RBF approximation using neural networks |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2210.16945 |