Description

The Fundamental Diagram (FD) is the empirical or analytical relationship between local pedestrian density and either walking speed or volumetric flow. Together, ρ–v and ρ–q curves summarise macroscopic crowd behaviour: free-flow at low density, congestion above a critical density, jamming and the "faster-is-slower" regime above that. In the thesis context, the FD is the bridge between BLE-derived ground-truth trajectories and CSI-derived density observations — it constrains the physics-informed model to obey conservation of pedestrians.

When it's used

  • Calibrating continuum-crowd-model and social-force-model parameters
  • Validating crowd-flow-estimation outputs against ground truth
  • Capacity analysis for indoor venues
  • Regulariser inside physics-informed CSI inference

Limitations

  • Strongly population-dependent (geography, age, culture)
  • Anisotropy (uni- vs bi-directional flow) changes the curves
  • Hard to fit at extreme densities without dedicated experiments

Source Papers

  • di2023_285b — physics-informed FD in crowd modelling
  • wolinski2014_f409 — FD-based crowd-simulator calibration
  • jebrane2026_3e34 — FD validation in agent-based simulation
  • maity2024_4dd4 — FD in continuum pedestrian flow
  • porzycki2023_6cf3 — FD-driven evacuation calibration

8 vault papers use this method

Titles and DOIs only — no abstracts, no analyses.

  • Physics-Informed Deep Learning for Traffic State Estimation: A Survey and the Outlook 2023 DOI ↗
  • Data-driven Crowd Modeling Techniques: A Survey 2022 DOI ↗
  • A hybrid mesoscopic/agent-based model for crowd dynamics with emotional contagion 2026 DOI ↗
  • Modeling spatial patterns in a moving crowd of people using data-driven approach—A concept of Interplay Floor Field 2023 DOI ↗
  • Physics of Human Crowds 2023 DOI ↗
  • Crowds in Equations 2018 DOI ↗
  • Continuum theory for pedestrian traffic flow: Local route choice modelling and its implications 2015 DOI ↗
  • Basics of modelling the pedestrian flow 2006 DOI ↗