<p>We propose a weighted nonlinear reservoir computing (WNLRC) method that enhances the state update dynamics by incorporating nonlinear transformations of the reservoir node states and aggregating information from neighboring nodes based on the reservoir’s network structure, thereby significantly improving the nonlinear learning capacity of reservoir computing (RC) for complex chaotic systems. Specifically, we employ polynomial nonlinear transformations. Given that the predictive performance of machine learning methods, particularly RC, is highly sensitive to key parameters, we utilize the Bayesian optimization algorithm to optimize the model’s parameters. To evaluate the prediction performance of the proposed WNLRC model, we perform simulation experiments on the Mackey-Glass and Rössler chaotic systems, comparing the results with those of representative baseline RC models and deep learning models. The WNLRC model demonstrates superior prediction accuracy and stability in long-term forecasting, exhibiting robust performance under varying noise levels and initial conditions. It consistently outperforms baseline models and maintains high prediction accuracy even with smaller training sets, underscoring its effectiveness and reliability across diverse tasks and conditions. Given its exceptional performance in predicting chaotic systems, the WNLRC model holds great potential for widespread application in time series forecasting in the future.</p>