Evolutionary algorithms that generate recurrent neural networks for learning chaos dynamics

Research on recurrent neural networks using evolutionary algorithms has begun with the aim of reducing the workload of network designers. Nevertheless, there have so far been no examples of studies of the non-periodic time series problem for which the recurrent neural networks are needed. We treat the synthesis of recurrent neural networks for the study of chaos dynamics using previously proposed two-dimensional genetic algorithms (2-D GAs). The 2D genetic algorithms are an extension of genetic programming to the synthesis of neural networks. The Lorenz orbit used as the training signal is normally a non-periodic orbit that undergoes continuous chaotic change. Accordingly, a recurrent neural network synthesized by a 2D GA is normally in the learning process. It is demonstrated that the output of a recurrent neural network that has a learning process synthesized by a 2D GA represents changes from a fixed point to a limit cycle and then changes again to the Lorenz attractor. That is to say, it is demonstrated that the hidden order of chaos dynamics can be learned. In future work we plan to perform experiments using more complex problems to verify the adaptability of neural networks synthesized with 2D GA.