A Gravity-informed Spatiotemporal Transformer for Human Activity Intensity Prediction

-- Human activity intensity prediction is crucial to many location - based services. Despite tremendous p rogress in modeling d ynamics 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 integrat ing the universal law of gravitation to refin e 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 physic al constrain t, 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 . Index Terms -- Human activity intensity prediction; Gravity model; Spatial interaction; Physics - informed machine learning; Over - smoothing phenomenon; Spatiotemporal graph neural network . This work is supported by the National Natural Science Foundation of China ( Grant # 42430106, 42371468, 424B2013) . Y i Wang, Zhenghong Wang, Fan Zhang, Chengling Tang, Weiyu Zhang and Yu Liu are with Institute of Remote Sensing and Geographic Information System, School of Earth and Space Sciences, Peking University, Beijing 100871, China. Chaogui Kang is with National Engineering Research Center of Geographic Information System, China University of Geosciences (Wuhan) 430074, China. Sijie Ruan is with School of Computer Science and Technology, Beijing Institute of Technology, Beijing 100081, China . Di Zhu and Zhongfu Ma are with Department of Geography, Environment and Society, University of Minnesota, Twin Cities, Minneapolis, MN 55455, USA . Y u Zheng is with JD iCity, JD Technology, Beijing 100176, China . P hilip S. Yu is with Department of Computer Science, University of Illinois Chicago, Chicago 60607, USA .