  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.
