Growing evolutional deep echo state network

Deep echo state network (Deep ESN) is a powerful method for time-series prediction, but developing the optimal structure of Deep ESN remains challenging. A novel generative framework, growing evolutional Deep ESN (GE Deep ESN) is proposed, where networks are generated through alternating growth and evolution. A model compression method is implemented during the evolution phase to optimize the inner structure of the reservoirs, and to automatically determine reservoir size. A simple termination criterion of growth is introduced to determine network depth. The feasibility and superiority of GE Deep ESN were validated experimentally with two benchmark prediction tasks. For real-time trajectory prediction in photoelectric tracking systems, an iterative learning model based on GE Deep ESN is proposed, the real time prediction result showed that network evolution enhances the model’s suitability for this task, and improves prediction precision. •A novel generative framework, GE Deep ESN, was introduced, allowing flexible specification of reservoir size. The internal structures of the reservoirs are optimized through an evolutionary process with a priori direction, and network depth is determined automatically using a straightforward termination criterion.•A termination criterion based on maximum neuronal similarity was proposed for network growth. This approach requires minimal computational resources and is not error-driven, enabling efficient selection of network depth parameters without repetition.•An iterative learning prediction model for dynamic real-time prediction was developed. This model adaptively improves the internal structure of GE Deep ESN based on incoming data, enhancing prediction accuracy.