An echo state network with interacting reservoirs for modeling and analysis of nonlinear systems

Jianming Liu, Xu Xu, Quan Bing Eric Li

Research output: Contribution to journalArticlepeer-review


The original echo state network only has one reservoir, which results in limited representation ability of the model. Existing multiple reservoirs models employ a unidirectional structure, wherein signals are transmitted from one reservoir layer to another along a specific direction without any interaction between them. Therefore, it naturally leads ones to consider the following fundamental question: Is it possible to establish a structure for the interaction between reservoirs? We will provide a positive answer in this paper. To be more precise, an echo state network with interacting reservoirs (Inter-ESN) is proposed for more effective modeling and analysis of nonlinear systems. Inter-ESN comprises two reservoirs, both receiving input information at each time. Meanwhile, the internal states of the two reservoirs are transmitted to each other during the evolution process. The unique structural design empowers the proposed model to generate more intricate reservoir states and more impactful feature representations, it also enhances the model’s short-term memory capacity, thereby significantly improving overall performance. The numerical experiments conducted on the MIT-BIH Arrhythmia Database, Charney–DeVore system, Lorenz system, and Kuramoto–Sivashinsky system demonstrate that Inter-ESN surpasses other models in performance.
Original languageEnglish
Pages (from-to)8341–8361
JournalNonlinear Dynamics
Publication statusPublished - 5 Apr 2024


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