Filling the historical data gap in peri-metropolitan vacant courtyards: a high-precision temporal reconstruction via a retrospective prediction model

Vacant courtyards (VCs) reflect cumulative outcomes of historical evolution and socioeconomic changes, yet their analysis remains hampered by data scarcity and methodological limitations. This study develops a retrospective prediction model integrating courtyard footprint extraction with township-level census data to reconstruct historical VC patterns in Beijing’s Miyun District. Results demonstrate that: (i) our model accurately predicts historical VC levels with superior data reliability and spatial generalizability; (ii) VCs increased by 104.66% to 32,615 between 2000 and 2020, reaching a 30.02% vacancy rate and displaying a ‘dense-center, sparse-wings’ spatial pattern influenced by topography and transportation networks; and (iii) VC evolution follows a ‘from early scattered distribution, to traffic corridor clustering, and ultimately to gradient diffusion toward peripheral areas’ trajectory with distinct growth phases. These findings provide a scientific foundation for targeted policy interventions, land allocation optimization, and predictive frameworks promoting sustainable urban-rural integration and effective VC reutilization.