Using a snow ablation optimizer in an autonomous echo state network for the model-free prediction of chaotic systems

The metaheuristic optimization algorithm (MHOA) is a type of automated tuning algorithm based on biological, physical or social behavior in nature that is widely used in the global optimization of complex problems. The autonomous echo state network (AESN) achieves superior performance in the model-free prediction of chaotic systems. However, hyperparameter setting is typically based on empirical values and selected through trial and error. Therefore, this paper emphasizes the importance of hyperparameter optimization of the AESN and clarifies the mechanism of using the MHOA. We incorporate the snow ablation optimizer (SAO) to optimize the hyperparameters of the AESN, referring to the prediction method as AESN-SAO. To explore the application prospect of the MHOA in the model-free prediction of chaotic systems, four MHOAs (chaotic coyote optimization, grey wolf optimizer, selective opposition grey wolf optimization and marine predator algorithm) are selected for comparative experiments in four chaotic systems (Rössler system, Colpitts oscillator, Lorenz-63 system and climate Lorenz-63 system). In accordance with the results of the experiments, the valid prediction time of the proposed AESN-SAO method reaches 11.94, 9.91, 15.73 and 7.14 Lyapunov times for the four chaotic systems. This study demonstrates that the SAO is an effective fusion strategy for reducing computational resource usage, while enhancing the time evolution performance and robustness of chaotic systems.