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The choice of the shape parameter highly effects the behaviour of radialbasis function (RBF) approximations, as it needs to be selected to balancebetween ill-condition of the interpolation matrix and high accuracy. In thispaper, we demonstrate how to use neural networks to determine the shapeparameters in RBFs. In particular, we construct a multilayer perceptron trainedusing an unsupervised learning strategy, and use it to predict shape parametersfor inverse multiquadric and Gaussian kernels. We test the neural networkapproach in RBF interpolation tasks and in a RBF-finite difference method inone and two-space dimensions, demonstrating promising results.

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