Echo state networks with double-reservoir for time-series prediction

In this paper, a novel model, named double-reservoir echo state networks (DR-ESN), is proposed. DR-ESN is constructed by two reservoirs which are connected in series, thus the performance of abstracting the characteristics from the prediction task is improved. A sufficient condition is provided to ensure the stability of DR-ESN. The batch gradient method and ridge regression method are utilized to optimize the six parameters of DR-ESN and train the readouts, respectively. DR-ESN is verified by two different experiments, chaotic time series prediction and real-valued function time series prediction. The simulation results demonstrates that DR-ESN has a more precise result than leaky-ESN in predicting the time series.