A Data-driven Crowd Simulation Framework Integrating Physics-informed Machine Learning with Navigation Potential Fields

Crowd simulation plays a crucial role in the prevention and management of public safety events in cities. However, the inherent complexity and diverse nature of human behaviors present substantial challenges in developing realistic and precise simulation models. Traditional rule-based physical models are limited by their reliance on fixed physical formulas and parameters, which hinders their ability to effectively handle the complex tasks associated with crowd simulation. Although deep learning methods have emerged as a promising solution, existing approaches largely emphasize pedestrian trajectory generation while struggling with interpretability and real-time dynamic simulation requirements. To address the aforementioned issues, we propose a novel data-driven crowd simulation framework that integrates physics-informed machine learning (PIML) with navigation potential fields. Our approach takes advantage of the strengths of both physical models and PIML. Specifically, we design an innovative physics-informed spatial-temporal graph convolutional network (PI-STGCN) as a data-driven module. Leveraging PI-STGCN, pedestrian movement trends can be accurately predicted in real-time during the simulation. Additionally, we construct a physical model of navigation potential fields based on flow field theory to guide pedestrian movements, thereby reinforcing physical constraints during the simulation. In our framework, navigation potential fields are dynamically computed and updated based on the movement trends predicted by the PI-STGCN, while the updated crowd dynamics, guided by these fields, subsequently feed back into the PI-STGCN. Comparative experiments on two publicly available large-scale real-world datasets across five scenes demonstrate that our proposed framework outperforms existing rule-based methods in both accuracy and fidelity. The similarity between the simulated and actual pedestrian trajectories improves by 10.8%. Furthermore, our framework exhibits enhanced adaptability and superior interpretability compared with methods that rely solely on deep learning for trajectory generation.