Dynamical system modelling using radial basis functions

The problem of modelling complex, chaotic dynamical systems is considered. A radial basis function (RBF) neural network is used to learn the system dynamics, and is then operated in free-running mode to generate time series which have very similar dynamical properties to those of the original training data. In our RBF network it is possible to fix the centre positions on a data-independent hyper-lattice which implies that only the linear-in-the-parameters weights need to be learnt for each different systems. This leads to a compact, efficient structure which, with regularisation applied to the learning of the weights, produces a correct, stable output. The dynamics of the synthesised system are verified by examining both the correlation dimension and Lyapunov exponents