Physics-infused Machine Learning for Crowd Simulation

Crowd simulation acts as the basic component in traffic management, urban planning, and emergency management. Most existing approaches use physics-based models due to their robustness and strong generalizability, yet they fall short in fidelity since human behaviors are too complex and heterogeneous for a universal physical model to describe. Recent research tries to solve this problem by deep learning methods. However, they are still unable to generalize well beyond training distributions. In this work, we propose to jointly leverage the strength of the physical and neural network models for crowd simulation by a Physics-Infused Machine Learning (PIML) framework. The key idea is to let the two models learn from each other by iteratively going through a physics-informed machine learning process and a machine-learning-aided physics discovery process. We present our realization of the framework with a novel neural network model, Physics-informed Crowd Simulator (PCS), and tailored interaction mechanisms enabling the two models to facilitate each other. Specifically, our designs enable the neural network model to identify generalizable signals from real-world data better and yield physically consistent simulations with the physical model's form and simulation results as a prior. Further, by performing symbolic regression on the well-trained neural network, we obtain improved physical models that better describe crowd dynamics. Extensive experiments on two publicly available large-scale real-world datasets show that, with the framework, we successfully obtain a neural network model with strong generalizability and a new physical model with valid physical meanings at the same time. Both models outperform existing state-of-the-art simulation methods in accuracy, fidelity, and generalizability, which demonstrates the effectiveness of the PIML framework for improving simulation performance and its capability for facilitating scientific discovery and deepening our understandings of crowd dynamics. We release the codes at https://github.com/tsinghua-fib-lab/PIML.