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Learning Extremely High Density Crowds as Active Matters
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Learns extremely high-density crowd dynamics from in-the-wild optical flow by combining a learnable active-matter continuum model (crowd material stress plus Toner-Tu active forces) with a differentiable Material Point Method, yielding a neural SDE that forecasts and simulates crowds.
Problem
Analyzing and forecasting extremely high-density crowds (at least 5 people/m²) from low-quality in-the-wild videos, where individuals cannot be tracked or counted and existing agent-based or black-box methods fail.
Approach
Models crowds as an active-matter continuum ("crowd material") with a learnable stress capturing elastic asymmetry, exponential resistance and compression dominance, plus learnable stochastic active forces from the Toner-Tu equation, solved with a novel Eulerian-Lagrangian MPM (CrowdMPM) whose particles are individuals and whose parameters are learned by neural networks from optical flow.
Key results
- On Drill2 the method improves Errvel and Errflow by up to 18.69% and 12.11% over baselines, and achieves the best results on most datasets except Hajj where SimVP is slightly better.
- In Drill1 and Marathon it obtains the best Errvel and second-best Errflow.
- Trained on Drill1, performance degrades consistently as tested behavior shifts from peaceful to neutral to aggressive (Drill2 then Drill3).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use CrowdMPM instead of TAU | high-density crowd prediction · Drill1 | Errvel: 0.5330 -> 0.5284 | Helped |
| Use CrowdMPM instead of HINN | high-density crowd prediction · Drill1 | Errflow: 0.9224 -> 0.9293 | Hurt |
| Use CrowdMPM instead of HINN | high-density crowd prediction · Drill2 | Errvel: 1.1187 -> 1.0721 | Helped |
| Use CrowdMPM instead of HINN | high-density crowd prediction · Drill2 | Errflow: 1.6603 -> 1.6558 | Helped |
| Use CrowdMPM instead of PredRNNv2 | high-density crowd prediction · Drill3 | Errvel: 1.6613 -> 1.6461 | Helped |
| Use CrowdMPM instead of PredRNNv2 | high-density crowd prediction · Drill3 | Errflow: 2.8734 -> 2.7354 | Helped |
| Use CrowdMPM instead of SimVP | high-density crowd prediction · Hajj | Errvel: 0.6212 -> 0.6591 | Hurt |
| Use CrowdMPM instead of SimVP | high-density crowd prediction · Hajj | Errflow: 0.9160 -> 0.9708 | Hurt |
| Use CrowdMPM instead of PredRNNv2 | high-density crowd prediction · Hellfest | Errvel: 3.3374 -> 3.0457 | Helped |
| Use CrowdMPM instead of BaselineI | high-density crowd prediction · Hellfest | Errflow: 5.2745 -> 4.8823 | Helped |
| Use CrowdMPM instead of SimVP | high-density crowd prediction · Marathon | Errvel: 1.6636 -> 1.4927 | Helped |
| Use CrowdMPM instead of SimVP | high-density crowd prediction · Marathon | Errflow: 10.633 -> 10.794 | Hurt |
Surprising findings
- On Marathon, the pure data-driven approach fits optical flow better than the proposed method, because the physics model filters noisy flow in the P2G step.
- On Hajj, the proposed method is slightly worse than SimVP, attributed to the peaceful, slowly moving crowd being an easier prediction task.
Limitations
- Single-view video input restricts cross-view generalization.
- Does not explicitly model queuing, grouping, lane formation, or other space users such as vehicles.
- Predicting entirely unseen scenes and crowds remains an open challenge; model is not suitable for low-density crowds.
Experimental setup
Datasets: Evacuation drills Hajj Hellfest Marathon
Benchmarks: Evacuation drills (Drill1-3) Hajj Hellfest Marathon
Metrics: MSE on velocity field (Errvel) MSE on optical flow (Errflow)
Baselines: PredFlow BaselineI PredRNNv2 SimVP TAU HINN
Builds on: Toner-Tu equation Material Point Method HINN Continuous Convolution
Closest papers by meaning
- STDDN: A Physics-Guided Deep Learning Framework for Crowd Simulation (ICLR 2026 · similarity 0.87)
- CrowdDiff: Multi-hypothesis Crowd Density Estimation using Diffusion Models (CVPR 2024 · similarity 0.84)
- Social Physics Informed Diffusion Model for Crowd Simulation (AAAI 2024 · similarity 0.84)
- Continuous Locomotive Crowd Behavior Generation (CVPR 2025 · similarity 0.83)
- Gaussian Density Splatting Network (NeurIPS 2026 · similarity 0.83)
- Learning Physics From Video: Unsupervised Physical Parameter Estimation for Continuous Dynamical Systems (CVPR 2025 · similarity 0.82)
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