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.

翻译：形状参数的选择对辐射基函数(RBF)近似(RBF)的行为产生高度影响,因为需要选择它来平衡内推矩阵和高精度之间的不准确性。在本文件中,我们展示了如何使用神经网络来确定RBF的形状参数。特别是,我们用未经监督的学习策略来构建一个经过培训的多层感应器,并用它来预测反多方和高斯内核的形状参数。我们在RBF的内插任务和RBF的极限差异方法中测试神经网络方法,展示出有希望的结果。