论文标题
使用神经网络的RBF近似的新变量形状参数策略
A new variable shape parameter strategy for RBF approximation using neural networks
论文作者
论文摘要
形状参数的选择高度影响径向基函数（RBF）近似的行为，因为需要选择它以平衡插值矩阵的不良条件和高精度。在本文中，我们演示了如何使用神经网络来确定RBF中的形状参数。特别是，我们构建了一种使用无监督的学习策略训练的多层感知器，并使用它来预测逆多Quastric和Gaussian核的形状参数。我们在RBF插值任务中测试了神经网络方法，以及一个和两个空间维度的RBF-FINITE差异方法，证明了令人鼓舞的结果。
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.
