Description
Continuum crowd models treat the crowd as a fluid: the state is a density field ρ(x, t) and a velocity field v(x, t), evolving under conservation of mass and a closure relation linking velocity to density (typically a fundamental-diagram). Hughes' dynamic continuum model adds a potential function so agents follow steepest-descent paths to exits. This family is the natural macroscopic counterpart to microscopic ABMs and is the closest match to the "crowd as liquid" thesis hypothesis.
When it's used
- Macroscopic pedestrian-flow PDEs in indoor evacuation studies
- Closing the loop between CSI density observations and BLE trajectory ground truth
- Physics-informed regularisation for learned crowd estimators
- Large-area simulations where particle-level fidelity is too expensive
Limitations
- Loses individual identity — useless for tracking-aware tasks
- Closure relations are hand-picked; no canonical "correct" choice
- PDE solvers introduce numerical diffusion that can mask real signal