Hydrodynamics-Informed Neural Network for Simulating Dense Crowd Motion Patterns

With global occurrences of crowd crushes and stampedes, dense crowd simulation has been drawing great attention. In this research, our goal is to simulate dense crowd motions under six classic motion patterns, more specifically, to generate subsequent motions of dense crowds from the given initial states. Since dense crowds share similarities with fluids, such as continuity and fluidity, one common approach for dense crowd simulation is to construct hydrodynamics-based models, which consider dense crowds as fluids, guide crowd motions with Navier-Stokes equations, and conduct dense crowd simulation by solving governing equations. Despite the proposal of these models, dense crowd simulation faces multiple challenges, including the difficulty of directly solving Navier-Stokes equations due to their nonlinear nature, the ignorance of distinctive crowd characteristics which fluids lack, and the gaps in the evaluation and validation of crowd simulation models. To address the above challenges, we build a hydrodynamic model, which captures the crowd physical properties (continuity, fluidity, etc.) with Navier-Stokes equations and reflects the crowd social properties (sociality, personality, etc.) with operators that describe crowd interactions and crowd-environment interactions. To tackle the computational problem, we propose to solve the governing equation based on Navier-Stokes equations using neural networks, and introduce the Hydrodynamics-Informed Neural Network (HINN) which preserves the structure of the governing equation in its network architecture. To facilitate the evaluation, we construct a new dense crowd motion video dataset called Dense Crowd Flow Dataset (DCFD), containing six classic motion patterns (line, curve, circle, cross, cluster and scatter) and 457 video clips, which can serve as the groundtruths for various objective metrics. Numerous experiments are conducted using HINN to simulate dense crowd motions under six motion patterns with video clips from DCFD. Objective evaluation metrics that concerns authenticity, fidelity and diversity demonstrate the superior performance of our model in dense crowd simulation compared to other simulation models. Our code and dataset are available at https://github.com/shanshan-zys/HINN.