Nonlinear curve fitting to stopping power data using RBF neural networks

• We present a novel method using an RBF neural network with an additional linear term.
• A simple and accurate empirical formula is developed for stopping power data, based on RBF.
• A benchmark dataset is tested with the new method.
• Additional linear term improves fitting accuracy.
• The new method can be used to fit various types of data- many applications in engineering.

This paper presents a novel approach for fitting experimental stopping power data to a simple empirical formula. The unknown complex nonlinear stopping power function is approximated by a Radial Basis Function (RBF) neural network with an additional linear neuron. The fitting coefficients are determined by learning algorithms globally. The experiments using the proposed method have been conducted on a benchmark dataset (titanium heat) and a set of stopping power data with implicit noise (MeV projectiles of Li, B, C, O, Al, Si, Ar, Ti and Fe in elemental carbon materials) from high energy physics measurements. The results not only showed the effectiveness of our method but also showed the significant improvement of fitting accuracy over other methods, without increasing computational complexity. The proposed approach allows us to obtain a fast and accurate interpolant that well suits to the situations where no stopping power data exist. It can be used as a standalone method or implemented as a sub-system that can be efficiently embedded in an intelligent system for ion beam analysis techniques.