Non-Linear Dynamic Modelling with Neural Networks
José Carlos Príncipe, Ludong Wang, Jyh-Ming Kuo · Applied and numerical harmonic analysis · 1998
This paper discusses the use of artificial neural networks (ANNs) for dynamic modelling of time series. We briefly present the theoretical basis for the modelling as a prediction of a vector time series in reconstructed space, and address the important role of the delay operator to implement Takens’ embedding theorem. Two types of dynamic models with vastly different topologies will be reviewed: the global models, and the local models. Global models can be built from multilayer perceptrons extended with memory structures. In order to train and test dynamic models, we argue that iterated prediction is more appropriate to capture the dynamics, because it imposes more constraints uring learning than single step prediction. We show how this method can be implemented by a recurrent ANN trained with trajectory learning. Local modelling partitions the phase space and each model specializes in the local dynamics. Each model can be rather simple and here linear models will be used. A modified Kohonen network is developed to first cluster and organize the trajectories in state space. We show that the weights of the Kohonen layer can be used directly to construct the local models. Experimental results corroborate the proposed methods.