Quantum-inspired pedestrian mobility modeling: Applying probabilistic spatial simulation to urban walkability and thermal comfort in Sri Lanka

Urban pedestrian movement is inherently uncertain, shaped by built form, microclimate, and time-varying crowding. This study develop a quantum-inspired probabilistic framework that models pedestrian presence as a spatial probability field derived from a composite potential integrating static structure (connectivity, crossings, barriers, visibility, points of interest) and dynamic drivers (crowd density, shade/thermal exposure). Applying the method to University Junction, Moratuwa, Sri Lanka, the study discretizes the domain to 5 m cells and 15-minute time bins, estimate factor weights via variational minimization, and solve an eigen-problem to obtain probability maps. The model reproduces diurnal reconfiguration of flows, concentrating midday probabilities in shaded, connected corridors and reducing presence on exposed verges. Link-level validation shows strong agreement with observed shares (Pearson's r ≈ 0.77 evening; ≈ 0.71-0.77 across periods) and realistic spatial autocorrelation. Scenario tests (temporary barriers, event footprints) re-equilibrate the probability field without retraining, revealing predictable re-routing to substitute corridors. Compared with a Boltzmann-type classical model and a space-syntax predictor, the proposed approach achieves higher fit and better spatial realism by explicitly encoding climate comfort and crowding. The framework yields policy-ready maps that support shade investment, crossing consolidation, and operational crowd management, providing an interpretable and transferable tool for assessing, managing, and allocating pedestrian space under uncertainty.