Optimized echo state network for error compensation based on transfer learning

Echo State Network (ESN) is widely applied in nonlinear system modeling, but its performance is often limited by a lack of error autocorrelation analysis, leading to reduced modeling accuracy. Existing extensions, such as SR-ESN and ERBM, primarily focus on structural optimization or feature representation but fail to effectively address autocorrelation errors. To overcome these limitations, we propose a Transfer Learning-based Echo State Network (TLESN) that compensates for errors in realtime to enhance prediction accuracy. The TLESN integrates a computing layer based on ESN and a compensation layer employing transfer learning, which dynamically adjusts output weights. To validate the proposed model, experiments are conducted on the Mackey-Glass time series, a practical Sunspot dataset, and a real-world industrial dataset. Results demonstrate that TLESN effectively mitigates autocorrelation errors, achieving at least a 17% improvement in prediction accuracy compared to existing ESN extensions. • Analyze the source error of ESN modeling accuracy and their impacts when there are autocorrelation errors. • Propose an error compensation strategy based on transfer learning to adjust to errors in real time. • TLESN has superior accuracy, robustness, and stability in nonlinear system modeling.