The nonlinear scale-matching mechanism of green innovation transfer: Insights from explainable machine learning

Addressing climate change and advancing the Sustainable Development Goals (SDGs) have positioned green innovation as a key driver of urban ecological transformation and regional competitiveness. Growing attention focuses on the mechanisms of green innovation transfer and diffusion among cities. Systematically uncovering patterns and mechanisms of green innovation collaboration across different city size combinations is crucial for understanding urban innovation network evolution and enhancing regional green innovation governance. Using data from 297 Chinese cities between 2001 and 2020, including intercity green patent transfers and other multi-source datasets, this study employs the eXtreme Gradient Boosting (XGBoost) machine learning model to systematically analyze the nonlinear effects of city size combinations on green innovation collaboration. The results indicate that China's Green Innovation Network (GIN) has evolved from concentration in core cities to a multi-centered, widely connected, and hierarchically coordinated structure. During this process, collaboration was influenced by nonlinear interactions of cities of different population sizes, exhibiting pronounced threshold stratification and staged transitions. Further analysis reveals that the optimal pairing patterns mainly involve diversified collaboration paths between medium-small and large cities, between medium-large and small cities, as well as between large city pairs. By contrast, the least favorable pairing occurs when the target city has a population between 1 and 3 million, a category that has long remained within a “low-efficiency cooperation zone.” This study enriches the theoretical framework of GIN and provides scientific evidence to support the optimization of regional green innovation policies and urban collaborative innovation strategies.