Human activity intensity prediction is a crucial to many location-based services. Although tremendous progress has been made to model dynamic spatiotemporal patterns of human activity, most existing methods, including spatiotemporal graph neural networks (ST-GNNs), overlook physical constraints of spatial interactions and the over-smoothing phenomenon in spatial correlation modeling. To address these limitations, this work proposes a physics-informed deep learning framework, namely Gravity-informed Spatiotemporal Transformer (Gravityformer) by refining transformer attention to integrate the universal law of gravitation and explicitly incorporating constraints from spatial interactions. Specifically, it (1) estimates two spatially explicit mass parameters based on inflow and outflow, (2) models the likelihood of cross-unit interaction using closed-form solutions of spatial interactions to constrain spatial modeling randomness, and (3) utilizes the learned spatial interaction to guide and mitigate the over-smoothing phenomenon in transformer attention matrices. The underlying law of human activity can be explicitly modeled by the proposed adaptive gravity model. Moreover, a parallel spatiotemporal graph convolution transformer structure 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 approach over state-of-the-art benchmarks. Additionally, the learned gravity attention matrix can be disentangled and interpreted based on geographical laws. This work provides a novel insight into integrating physical laws with deep learning for spatiotemporal predictive learning.
View on arXiv@article{wang2025_2506.13678,
title={ A Gravity-informed Spatiotemporal Transformer for Human Activity Intensity Prediction },
author={ Yi Wang and Zhenghong Wang and Fan Zhang and Chengling Tang and Chaogui Kang and Di Zhu and Zhongfu Ma and Sijie Ruan and Weiyu Zhang and Yu Zheng and Philip S. Yu and Yu Liu },
journal={arXiv preprint arXiv:2506.13678},
year={ 2025 }
}