## 1 Introduction
### Literature Review  
Scholars worldwide have conducted extensive research on elderly care facilities, primarily focusing on three dimensions: 1. [PERSON] et al. employed expert scoring to assess service models and quality [54], while [PERSON]'s team adopted questionnaire surveys to capture geriatric demand profiles [55]. 2. [PERSON] et al. [56] identified walking as the predominant travel mode for Spanish seniors aged 65 and over, a finding corroborated by [PERSON] et al. [57] in rural Jintang, China, where walking remains central to elderly mobility. 3. Studies by [PERSON] and [PERSON] et al. [55; 58] evaluated facility performance through service quality metrics and management models.  
Despite growing academic attention to population aging [59], existing studies present three main limitations: 1. Methodological Limitations: Traditional methods like expert scoring [11; 58] and questionnaires [60; 61] face challenges in capturing the dynamic evolution of elderly care demands during aging processes. Their reliance on static datasets and geographically constrained sampling frameworks limits cross-regional comparative analyses, particularly in disentangling urban-rural differentiation patterns of facility allocation [62]. 2. Spatial Synergy Neglect: [PERSON] et al.'s research [58] over-relies on static built environment analyses of care facilities themselves, with insufficient investigation into spatial synergies with surrounding functional facilities. 3. Behavior-Environment Mismatch: Current studies inadequately address behavioral characteristics of the elderly. Despite the urgent need for a comprehensive 15-min walkability assessment system for urban and suburban seniors, existing evaluation frameworks insufficiently incorporate both elderly walking capacity and street-built environment considerations.  
This study investigates elderly care facilities in Changsha through machine learning and multi-source data fusion, establishing a multidimensional walkability assessment system: 1. Spatial pattern analysis: The Random Forest algorithm was employed to decode spatial weight characteristics of facility locations in both urban and rural areas. This approach not only captures locational features of existing facilities but also effectively reveals urban-rural differentiation patterns, overcoming traditional methods' over-reliance on expert experience. 2. Spatial synergy evaluation: Walkability scores and static decay functions were integrated to analyze spatial coordination between elderly care facilities and surrounding service infrastructure from pedestrian accessibility perspectives. 3. Micro-environment analysis: Streetscape semantic segmentation techniques were applied to extract urban streetscape elements, with regression analyses quantifying micro-scale impacts of built environments on walkability scores. Combined with Random Forest predictions, streetscape and demographic data enabled optimization simulations for facility distribution under urban-rural divergence scenarios.  
Methodologically, this framework enhances spatiotemporal adaptability in facility assessment, identifies supply-demand mismatch hotspots, and provides scientific references for future facility siting. Theoretically, it enriches healthy city theories by incorporating elderly mobility constraints. Practically, the findings provide actionable insights for designing age-friendly urban-rural landscapes, optimizing equitable resource distribution, and enhancing societal well-being--offering critical policy pathways to address spatial inequities in aging societies.