Mapping Chinese urban carbon emissions with a graph-based multi-branch deep learning framework

Urban carbon emissions have emerged as a central challenge for sustainable development in China. Existing statistical and machine learning approaches, however, face limitations in capturing spatial heterogeneity and historical dynamics of urban emissions. To overcome these challenges, this study developed Carbon Graph Multi-branch Network (CGMN), a graph-based deep learning framework that integrates spatial relationships, temporal dependencies, and multi-source urban features for urban carbon emissions estimation. Given the scarcity of labeled city-level emissions, a composite loss framework is designed to incorporate both strong and weak supervision, enhancing the model’s consistency, generalization, and robustness. We also developed a spatial mismatch index between emissions and Gross Domestic Product (GDP) to investigate the evolving relationship between urban carbon emissions and economic activity. The proposed CGMN achieves robust predictive performance (R² = 0.79; RMSE = 10.63; MAE = 8.31; WAPE = 27.51), demonstrating its capability to capture the contributions of key driving factors. Feature importance analysis reveals that economic structure is the dominant determinant of urban carbon emissions, accounting for 32% of the total feature contribution. From 2000 to 2021, China’s urban carbon emissions increased rapidly until around 2012 before stabilizing, with an average annual growth rate of 5.7%. The spatial mismatch analysis reveals pronounced regional disparities: low-mismatch cities decreased by 53%, mainly in western and central regions, while high-mismatch cities increased by 35%, concentrated in eastern coastal areas. These results provide a scientific basis for understanding the spatiotemporal evolution of China’s urban carbon emissions and offer insights for promoting coordinated economic and low-carbon development.