An echo state network based on enhanced intersecting cortical model for discrete chaotic system prediction - Wang, Xubin; Ma, Pei; Lian, Jing; Liu, Jizhao; Ma, Yide (Frontiers in Physics, 2025)
IntroductionThe prediction of chaotic time series is a persistent problem in various scientific domains due to system characteristics such as sensitivity to initial conditions and nonlinear dynamics. Deep learning models, while effective, are associated with high computational costs and large data requirements. As an alternative, Echo State Networks (ESNs) are more computationally efficient, but their predictive accuracy can be constrained by the use of simplistic neuron models and a dependency on hyperparameter tuning.MethodsThis paper proposes a framework, the Echo State Network based on an Enhanced Intersecting Cortical Model (ESN-EICM). The model incorporates a neuron model with internal dynamics, including adaptive thresholds and inter-neuron feedback, into the reservoir structure. A Bayesian Optimization algorithm was employed for the selection of hyperparameters. The performance of the ESN-EICM was compared to that of a standard ESN and a Long Short-Term Memory (LSTM) network. The evaluation used data from three discrete chaotic systems (Logistic, Sine, and Ricker) for both one-step and multi-step prediction tasks.ResultsThe experimental results indicate that the ESN-EICM produced lower error metrics (MSE, RMSE, MAE) compared to the standard ESN and LSTM models across the tested systems, with the performance difference being more pronounced in multi-step forecasting scenarios. Qualitative analyses, including trajectory plots and phase-space reconstructions, further support these quantitative findings, showing that the ESN-EICM's predictions closely tracked the true system dynamics. In terms of computational cost, the training phase of the ESN-EICM was faster than that of the LSTM. For multi-step predictions, the total experiment time, which includes the hyperparameter optimization phase, was also observed to be lower for the ESN-EICM compared to the standard ESN. This efficiency gain during optimization is attributed to the model's intrinsic stability, which reduces the number of divergent trials encountered by the search algorithm.DiscussionThe results indicate that the ESN-EICM framework is a viable method for the prediction of the tested chaotic time series. The study shows that enhancing the internal dynamics of individual reservoir neurons can be an effective strategy for improving prediction accuracy. This approach of modifying neuron-level complexity, rather than network-level architecture, presents a potential direction for the design of future reservoir computing models for complex systems.