ELHINN: Unifying Dense Crowd Simulation Across Scales via Eulerian–Lagrangian Hydrodynamics

Developing effective dense crowd simulation is challengingdue to the scale gap between macroscopic collective coherence and mi-croscopic individual realism. Existing macroscopic (Eulerian) methodscapture global motion patterns but lack individual trajectories, whereasmicroscopic (Lagrangian) methods model individual behaviors yet oftenfail to preserve systemic consistency in dense scenarios. To address this,we propose the Eulerian–Lagrangian Hydrodynamics-Informed NeuralNetwork (ELHINN), a unified cross-scale framework that couples macro-scopic velocity evolution with microscopic trajectory refinement by usingevolved Eulerian velocity fields as physical priors to guide Lagrangian tra-jectories. For velocity evolution, we develop an enhanced Hydrodynamics-Informed Neural Network (HINN++) that incorporates a learnable gov-erning equation with Kolmogorov–Arnold Network (KAN) residual cor-rection and environmental boundary conditions, enabling accurate mod-eling of complex nonlinear dynamics under varying scenarios. For tra-jectory refinement, we use a Physics-Informed Neural Network (PINN)augmented with an entrance-aware resampling strategy (EARS) andcollision-avoidance constraints to ensure stability and fidelity. Experi-ments on two real-world crowd datasets demonstrate that ELHINN out-performs existing methods in simulating dense crowds across both scales.Codes are available at https://github.com/shanshan-zys/ELHINN.