融合物理模型与机器学习，实现更真实可解释的群体动态模拟。

Traditional rule-based physical models are limited by their reliance on singular physical formulas and parameters, making it difficult to effectively tackle the intricate tasks associated with crowd simulation. Recent research has introduced deep learning methods to tackle these issues, but most current approaches focus primarily on generating pedestrian trajectories, often lacking interpretability and failing to provide real-time dynamic simulations.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 leverages the strengths of both physical models and PIML. Specifically, we design an innovative Physics-informed Spatio-temporal Graph Convolutional Network (PI-STGCN) as a data-driven module to predict pedestrian movement trends based on crowd spatio-temporal data. 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 accuracy and fidelity. The similarity between simulated and actual pedestrian trajectories increases by 10.8%, while the average error is reduced by 4%. Moreover, our framework exhibits greater adaptability and better interpretability compared to methods that rely solely on deep learning for trajectory generation.