arXiv subjects

Zhongfu Ma

Publications and source records attributed to Zhongfu Ma.

2 recordsLinked to original sources

arXiv2026

Discovering Governing Spatial Interaction Mechanisms in Dynamic Urban Systems

Governing equations are fundamental for describing and predicting dynamic urban geographic systems. Unlike physical systems guided by first principles, urban spatiotemporal phenomena emerge from coupled geographic processes that lack deterministic theoretical foundations, making the discovery of governing equations elusive and largely heuristic. Spatiotemporal dynamics in urban systems are often observed as sequential snapshot data of spatial distribution, while the cause of such dynamics is often implied or unknown. In this study, we propose a unified differential equation formalism that decomposes urban dynamics into a time-invariant spatial interaction process and a self-dynamic component. Building on this formalism, we introduce the Urban Discovery Framework (U-Discovery), which integrates hypothesis generation, neural fitting, and governing equation identification for the discovery of governing spatial interaction laws. U-Discovery leverages Large Language Models and literature-based reasoning to propose differential equation candidates. Each candidate was calibrated from the observed spatiotemporal dynamics using a neural fitting method. The candidates are evaluated and ranked based on the fitting error and mathematical complexity. Our synthetic experiments prove that U-Discovery can find the sole governing equation from the simulated dynamics. Empirical experiments in Hennepin County, Minnesota, further demonstrate the potential of U-Discovery in identifying optimal governing laws from real-world human activity dynamics.

physics.soc-ph↗

arXiv2025

A Gravity-informed Spatiotemporal Transformer for Human Activity Intensity Prediction

Human activity intensity prediction is crucial to many location-based services. Despite tremendous progress in modeling dynamics of human activity, most existing methods overlook physical constraints of spatial interaction, leading to uninterpretable spatial correlations and over-smoothing phenomenon. To address these limitations, this work proposes a physics-informed deep learning framework, namely Gravity-informed Spatiotemporal Transformer (Gravityformer) by integrating the universal law of gravitation to refine transformer attention. Specifically, it (1) estimates two spatially explicit mass parameters based on spatiotemporal embedding feature, (2) models the spatial interaction in end-to-end neural network using proposed adaptive gravity model to learn the physical constraint, and (3) utilizes the learned spatial interaction to guide and mitigate the over-smoothing phenomenon in transformer attention. Moreover, a parallel spatiotemporal graph convolution transformer is proposed for achieving a balance between coupled spatial and temporal learning. Systematic experiments on six real-world large-scale activity datasets demonstrate the quantitative and qualitative superiority of our model over state-of-the-art benchmarks. Additionally, the learned gravity attention matrix can be not only disentangled and interpreted based on geographical laws, but also improved the generalization in zero-shot cross-region inference. This work provides a novel insight into integrating physical laws with deep learning for spatiotemporal prediction.

cs.LG↗