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KY: Kybernetik

KY 2: Dynamische Systeme | Neuronale Netzwerke

KY 2.1: Vortrag

Dienstag, 16. März 1999, 09:00–09:45, ZO 3

Forecasting of Emergent Dynamical Systems by Recurrent Networks — •Hans-Georg Zimmermann and Ralph Neuneier — München

Feedforward neural networks try to solve the identification of a dynamical system as a pattern recognition approach. Recurrent neural networks allow the explicit modeling of the time structure by implementing a finite unfolding of the dynamical system over time. After discussing advantages and problems of this method, we propose a new technique of unfolding in space and time. One crucial new element is an additional transformation of the state space to extract more complex structure by approximating it with smooth functions. The new approach also gives a interesting insight in the tradeoff between nonlinearity and noise. Furthermore, we are able to characterize the dynamic of the system as stable, chaotic or emergent. For example, in the field of economy, there are many indicators to believe that dynamical markets are emergent systems which means that they stay close to the edge of chaos. We demonstrate the superior identification abilities of our new recurrent neural network by analyzing the exchange market DM-$ as an example of a complex dynamic system with respect to forecastability and stability. Hence, our article proposes an approach which integrates analysis of dynamical systems analysis, chaos theory, and new results within a neural network environment.