Deep echo state network with projection-encoding for multi-step time series prediction

Abstract

To fully utilize the advantage of reservoir computing in deep network modeling, a deep echo state network with projection-encoding (DEESN) is newly proposed for multi-step time series prediction in this paper. DEESN integrates multiple echo state network (ESN) modules and extreme learning machine (ELM) encoders in series arrays. Firstly, the $k$th ESN in DEESN learner is responsible for $k$th step ahead prediction. The forecast output and encoded reservoir states of the previous ESN module are concatenated with the input variable to form the new input signals for the next adjacent module. Therefore, the temporal dependency among future time steps can be learned, which contributes the performance improvement. Secondly, the ELM encoder is used to optimize the reservoir states for time consumption reduction. Finally, the effectiveness of DEESN is evaluated in artificial chaos benchmarks and real-world applications. Experimental results on six different datasets and comparative models demonstrate that the proposed DEESN has excellent accuracy and robust generalization for multi-step time series prediction.