An improved Gated Recurrent Unit model with hybrid network architecture for carbon emission forecasting in Zhejiang Province

To address the nonlinearity and non-stationarity of carbon emission time series and remedy the defects of existing hybrid models in parameter configuration and module coordination, this study develops a Bayesian Optimization-Variational Mode Decomposition-Convolutional Neural Network-Gated Recurrent Unit-Attention (BO–VMD–CNN–GRU-Attention) hybrid model for daily carbon emission forecasting in Zhejiang Province. The original carbon emission series is first decomposed into multiple subcomponents via entropy weight-based adaptive Variational Mode Decomposition (VMD). A Convolutional Neural Network (CNN) extracts local features, while a Gated Recurrent Unit (GRU) captures long-term temporal dependencies; the attention mechanism highlights key time steps, and Bayesian Optimization (BO) optimizes model hyperparameters jointly. Empirical results based on 2020–2025 Zhejiang daily carbon-emission data show that the proposed model achieves a mean squared error (MSE) of 504.86, a mean absolute percentage error (MAPE) of 1.44%, and a coefficient of determination R 2 of 0.9610, outperforming all baseline and advanced hybrid models on five out of six evaluation metrics. Wilcoxon signed-rank tests confirm that the improvements are statistically significant ( p < 0.01 for all pairwise comparisons). Ablation experiments confirm the synergistic effect of each module, and cross-provincial tests obtain R 2 over 0.95. Future 150-day predictions reveal cyclical fluctuations and a mild upward trend in regional carbon emissions. This framework provides reliable nonlinear time series forecasting support and quantitative references for targeted emission reduction policies.