The Impact of the Built Environment on Innovation Output in High-Density Urban Centres at the Micro-Scale: A Case Study of the G60 S&T Innovation Valley, China

The micro-scale interplay between the built environment and innovation has attracted increasing scholarly attention. However, discussions on how such microdynamics operate and vary across high-density cities remain insufficient. This study focuses on nine high-density urban centres along the G60 S&T Innovation Valley and employs a fine-grained grid unit, viz. 1 km × 1 km, combined with the gradient boosting decision tree (GBDT) model to address these issues. Results show that urban construction density-related variables, including the building density, floor area ratio, and transportation network density, generally rank higher than the amenity density and proximity-related variables. The former contributes 50.90% of the total relative importance in predicting invention patent application density (IPAD), while the latter two contribute 13.64% and 35.46%, respectively. Threshold effect analysis identifies optimal levels for enhancing IPAD. Specifically, the optimal building density is approximately 20%, floor area ratio is 5, and transportation network density is 8 km/km2. Optimal distances to universities, city centres, and transportation hubs are around 1 km, 17 km, and 9 km, respectively. Furthermore, significant city-level heterogeneity was observed: most density-related variables consistently have an overall positive association with IPAD, with metropolitan cities (e.g., Hangzhou and Suzhou) exhibiting notably higher optimal values compared to medium and small cities (e.g., Xuancheng and Huzhou). In contrast, the threshold effects of proximity-related variables on IPAD are more complex and diverse. These findings offer empirical support for enhancing innovation in high-density urban environments.