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Learning a robust shape parameter for RBF approximation
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DOI：10.1016/j.amc.2025.129706.png)
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Abstract
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• Shape parameter tuning is an open problem that appears in interpolation, kernel density estimation and meshless methods. • New optimization problem to find the shape parameter ε while controlling the condition number of the interpolation matrix A=. • Creation of a dataset to train a neural network that predicts the shape parameter ε given any set of points x‾⊂Rn of size N. • Novel fallback procedure to guarantee that the proposed shape parameter generates a well-posed interpolation matrix. • Method is evaluated for 1-dimensional and 2-dimensional problems in interpolation and numerical solution of PDEs.
Keywords:
Radial basis functions
Shape parameter
Machine learning
Finite difference
Interpolation
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