Evolutionary Echo State Network: A neuroevolutionary framework for time series prediction

Abstract

From one side, Evolutionary Algorithms have enabled enormous progress over the last years in the optimization field. They have been applied to a variety of problems, including optimization of Neural Networks’ architectures. On the other side, the Echo State Network (ESN) model has become increasingly popular in time series prediction, for instance when modeling chaotic sequences. The network has numerous hidden neurons forming a recurrent topology, so-called reservoir, which is fixed during the learning process. Initial reservoir design has mostly been made by human experts; as a consequence, it is prone to errors and bias, and it is a time consuming task.

In this paper, we introduce an automatic general neuroevolutionary framework for ESNs, on which we develop a computational tool for evolving reservoirs, called EVOlutionary Echo State Network (EvoESN). To increase efficiency, we represent the large matrix of reservoir weights in the Fourier space, where we perform the evolutionary search strategy. This frequency space has major advantages compared with the original weight space. After updating the Fourier coefficients, we go back to the weight space and perform a conventional training phase for full setting the reservoir architecture. We analyze the evolutionary search employing genetic algorithms and particle swarm optimization, obtaining promising results with the latter over three well-known chaotic time series. The proposed framework leads fast to very good results compared with modern ESN models. Hence, this contribution positions an important family of recurrent systems in the promising neuroevolutionary domain.