Description
Physics-Informed Deep Learning embeds physical conservation laws — typically as soft penalties on residuals of governing PDEs — into the training loss of a neural network, so that the learned function approximately respects those laws even where data is sparse. In crowd modelling, the relevant physics is the continuity equation (mass conservation) coupled with a fundamental-diagram closure. This is the theoretical backbone for the thesis's "crowd as liquid" framing.
When it's used
- Coupling CSI-derived density observations with conservation constraints
- Filling spatial gaps where sensors are sparse
- Producing physics-respecting forecasts in evacuation / event scenarios
Limitations
- Soft penalties do not strictly enforce the physics
- Training is slower and more sensitive to weighting than vanilla deep learning
- PDE choice and boundary conditions need careful design
Source Papers
- di2023_285b ↗ — physics-informed deep learning for crowd dynamics