Urban Vitality Within the Daily Activity System: Multidimensional Spatial Patterns and Nonlinear Relationships with the Built Environment in Nanjing, China

A B S T R A C TUrban vitality is crucial for sustainable development, yet holistic analysis within complex living contexts is lacking. This study addresses this gap by constructing a cognitive and analytical model from the perspective of daily activities, which can reflect the differentiation of activities and the integration of spatiotemporal information in the construction of urban vitality, as well as the more comprehensive and targeted built environment that supports vitality. Guided by this perspective, relying on multi-source geographic big data, and the CRITIC objective weighting method of element correlation, a comprehensive assessment of urban vitality is conducted to identify its multiple spatial patterns. Furthermore, a built environment indicator system that takes into account multiple spatial elements of materiality, sociality, place, and flow is constructed. Combined with the XGBoost-SHAP machine learning interpretable model, the nonlinear relationships between urban vitality and built environment are explored. Based on the empirical case of ' China Metropolis-Nanjing ', the following findings are obtained: (1) Activity-based analysis effectively reveals vitality spatial patterns and identifies threshold/interaction effects of the built environment. (2) Urban vitality shows significant spatial polarization with a core-periphery structure. Most areas lack multi-suitability of vitality, dominated by combined work and visit activity vitality. (3) Built environment factors linked to fundamental livelihood support (employment, leisure/shopping facilities) are strongly associated with vitality. Their type, scale, and level exhibit non-linear effects (positive/negative, varying strength) depending on specific intervals and interactions. Therefore, urban policies should dynamically address residents' spatiotemporal resource and environmental needs within actual living contexts to cultivate people-centric urban vitality.