Co-evolving data driven models and test data sets with the application to forecast chaotic time series

Abstract

Several approaches have been introduced for modeling and prediction of nonlinear dynamics which have chaotic characteristics. Among these methods, data driven approaches such as Auto Regressive (AR) models, Nonlinear Auto Regressive (NAR) models, Radial Basis Function (RBF) networks, and Multi Layered Perceptron (MLP) neural networks have proven themselves to be powerful approaches in modeling and prediction of chaotic dynamics. However, the structure of these models should be known before the training phase, which is a very complicated problem. In this research, we introduce a co-evolutionary approach for modeling and system identification of chaotic dynamics. The proposed algorithm is composed of two co-evolving populations: candidate data driven models, and test data sets which either extract new information from the nonlinear chaotic system or elicit desirable behavior from it. The fitness of candidate models is their ability to explain behavior of the target chaotic system observed in response to tests carried out so far by predicting the future values of these data sets; the fitness of candidate test data sets is their ability to make the models disagree in their predictions. To check the performance of this algorithm, three case studies are considered. First, we apply this method to approximate a static function which has complicated behavior near zero. Then, we use this algorithm to predict two bench mark time series in chaos literature: Sunspot Number (SSN) and Mackey-Glass (MG) time series. Simulation results depict the power of proposed method in modeling and predicting complicated nonlinear systems.