A Gravity-informed Spatiotemporal Transformer for Human Activity Intensity Prediction

2025-06-16

AI Summary

Human activity intensity prediction faces two key challenges: the absence of physical constraints in spatiotemporal modeling and oversmoothing in graph neural networks. To address these, we propose the Gravitation-guided Spatiotemporal Transformer (GST-Former), the first model to explicitly embed Newton’s law of universal gravitation into the attention mechanism—thereby encoding mass-dependent interaction strength and distance-decaying spatial influence. GST-Former introduces a decoupled, physics-consistent attention matrix and synergistically integrates parallel spatiotemporal graph convolutions with the Transformer architecture to enable closed-form spatial interaction modeling. Evaluated on six large-scale real-world datasets, it significantly outperforms state-of-the-art methods. Crucially, its learned attention weights strictly adhere to the geographic distance decay principle, achieving both superior predictive accuracy and explicit physical interpretability.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Computer Vision: Video Understanding & Activity Analysis

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

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.

Problem

• Overcoming physical constraints in human activity prediction
• Addressing over-smoothing in spatial correlation modeling
• Integrating gravity law with deep learning frameworks

Innovation

• Integrates gravity law into transformer attention
• Estimates mass parameters from inflow and outflow
• Uses parallel spatiotemporal graph convolution transformer