Quantifying Complex Urban Spillover Effects via Physics-based Deep Learning

Abstract Spillover effects are pervasive in a variety of natural, social, and physical environments, such as urban heat waves and human mobility dynamics. Quantifying spillover effects is crucial for understanding and predicting the complex processes that cascade through urban systems. Prior studies have relied on ad-hoc parameters and homogeneity assumptions in conventional physics of diffusion to capture spillover from immediate surroundings. These approaches, however, fall short of accounting for the spatial heterogeneity present in urban systems. Here, we introduce a novel physics-based deep learning model coupled with random diffusion, Deep Random Diffusion (DRD), that captures complex and nonlocal interactions by integrating observations from urban systems with the physics of diffusion derived from theoretical physics models. The proposed method, validated with natural and social system processes in five cities in the U.S., outperforms conventional models for all five cities. The experiments show that the spatial variances of complex natural environments and social systems are highly predictable at 60% − 86% by incorporating heterogenous spillovers. A general and consistent scale of spillover effects ranging from 0.7 to 1.2 km, is identified by the proposed model across cities, despite varying landscapes and geography. Integrating information from this scale of neighbors helps to reduce excessive reliance on individual variables in predictions, thereby preventing overestimation and underestimation at extreme values. The findings in this study not only untangle the complexity and improve the predictability of various urban phenomena but also provide transferrable new insights to inform effective solutions for adapting to urban stressors in different urban settings, such as extreme heat resulting from climate change.