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：形状参数的选择对径向基函数（RBF）近似的性能具有重要影响，因为其选取需要在插值矩阵的病态性与高精度之间取得平衡。本文阐述了如何利用神经网络来确定RBF中的形状参数。具体而言，我们构建了一个采用无监督学习策略训练的多层感知器，并利用它来预测逆多重二次核函数与高斯核函数的形状参数。我们在单维和二维空间中的RBF插值任务以及一种RBF-有限差分方法中测试了该神经网络策略，结果显示出良好的前景。