Multi-scale Radial Basis Function Networks

A novel modelling framework is proposed for constructing parsimonious and flexible radial basis function network (RBF) models. Unlike a conventional standard Gaussian kernel based RBF network, where all the basis functions have the same scale (kernel width), or each basis function has a single individual scale, the new network construction approach adopts multiscale kernels (with multiple kernel widths for each selected centre) as the basis functions to provide more flexible representations with better generalized properties for general nonlinear dynamical systems. A standard orthogonal least squares (OLS) algorithm is then applied to select significant model terms (basis functions) to obtain parsimonious models.