Sequence prediction with different dimensions based on two novel deep echo state network models

The echo state network (ESN) is a typical reservoir computation model, which was first proposed by Jaeger et al. It was widely used in various fields and achieved excellent results for a long time, especially in time series prediction. In recent years, there are few improvements to the ESN structure, and the more famous is the deep echo state network (DESN) model. However, a DESN will cause the loss of input data. How to effectively optimize the structure of ESN and how to scientifically add input data to deep echo are urgent problems to be solved. In this paper, we propose multi-reservoir ESN models based on how the input data participate in the system. Then, we use complex nonlinear chaotic systems with different dimensions to test our model. Finally, we compare it with the traditional model and the recently proposed model, and then find that our models have better predictive performance.