Multi-module echo state network with variable skip length for chaotic time series prediction

Echo state networks (ESNs) have been extensively applied in time series prediction problems. However, the memory-nonlinearity trade-off problem severely limits the ability of ESNs to deal with chaotic time series prediction problems. In this study, a multi-module echo state network with variable skip length (MESN-VSL) is proposed to address this problem. First, the reservoir is divided into a nonlinear mapping module and multiple linear memory modules based on the idea of memory and nonlinearity separation. This idea can effectively balance the memory-nonlinearity trade-off problems. Second, a multi-module mechanism with skip length is put forward to model the characteristics of chaotic time series. The skip length and the number of linear memory modules of the MESN-VSL model are automatically determined based on the idea of phase-space reconstruction. Finally, the experimental results further demonstrate that the MESN-VSL model is superior to some existing models in chaotic time series prediction.