Bayesian Curve Fitting Based on RBF Neural Networks

Abstract

In this article, we introduce a novel method for solving curve fitting problems. Instead of using polynomials, we extend the base model of radial basis functions (RBF) neural network by adding an extra linear neuron and incorporating the Bayesian learning. The unknown function represented by datasets is approximated by a set of Gaussian basis functions with a linear term. The additional linear term offsets the localized behavior induced by basis functions, while the Bayesian approach effectively reduces overfitting. The presented approach is initially utilized to assess two numerical examples, then further on the method is applied to fit a number of experimental datasets of heavy ion stopping powers (MeV energetic carbon ions in various elemental materials). Due to the linear correction, the proposed method significantly improves accuracy of fitting and outperforms the conventional numerical-based algorithms. Through the theoretical results, the numerical examples and the application of fitting stopping powers data, we demonstrate the suitability of the proposed method.