Understanding complex crowd dynamics with generative neural simulators

TL;DR

This paper tackles the challenge of understanding complex crowd dynamics by merging laboratory-like control with the statistical richness of large-scale real-world data through NeCS, a data-driven Neural Crowd Simulator. NeCS uses a graph-based neural architecture with a conditional variational autoencoder to model the acceleration distribution of each pedestrian conditioned on state, history, and neighbors, enabling stochastic, autoregressive trajectory generation. The authors validate NeCS against key statistical features of real crowds and employ virtual surrogate experiments to uncover vision-guided, topological N-body interactions, showing a saturation of interaction strength around $N^* \approx 12$ and a field-of-view constrained, top-$k$ interaction structure. These results demonstrate that neural simulators can provide data-driven physical insight and a scalable platform for controlled experiments in crowd dynamics, with potential applications to other active-matter systems.

Abstract

Understanding the dynamics of pedestrian crowds is an outstanding challenge crucial for designing efficient urban infrastructure and ensuring safe crowd management. To this end, both small-scale laboratory and large-scale real-world measurements have been used. However, these approaches respectively lack statistical resolution and parametric controllability, both essential to discovering physical relationships underlying the complex stochastic dynamics of crowds. Here, we establish an investigation paradigm that offers laboratory-like controllability, while ensuring the statistical resolution of large-scale real-world datasets. Using our data-driven Neural Crowd Simulator (NeCS), which we train on large-scale data and validate against key statistical features of crowd dynamics, we show that we can perform effective surrogate crowd dynamics experiments without training on specific scenarios. We not only reproduce known experimental results on pairwise avoidance, but also uncover the vision-guided and topological nature of N-body interactions. These findings show how virtual experiments based on neural simulation enable data-driven scientific discovery.

Figures (6)

• Figure 1: (A) Snapshot of a model simulation. Colored circles indicate positions of simulated pedestrians, black circles indicate pedestrian trajectories upon which the simulation is conditioned, dotted tails indicate a 10 second history out of the total 60 second simulation horizon. (B) Sketch of modeling approach. The model uses a message passing graph neural network to construct a representation of the current state. Randomness is modeled with latent variables at the individual level, conditioned on the constructed representation. The representation and latent variables are decoded to predict the next state. (C) Distribution over pedestrians' horizontal velocity component of both observations and simulated data. The black dotted line in the inset PDF plot indicates a fitted Gaussian distribution. (D) Fundamental diagram showing how pedestrian velocity decreases as density increases, for both simulated and observed data. The solid lines and markers indicate the mean velocity, while the shaded area and error bars indicate the standard deviation. (E) Virtual experiment measuring the social force on a pedestrian walking towards a crowd of $N$ static pedestrians. The plot shows the mean net force of the crowd on the pedestrian of the standard social force model, its top-$k$ variant, and of NeCS. The vertical dashed line indicates $N^* \approx 12$. The inset shows a sketch of the surrogate experiment setup (see Figure \ref{['fig:model-interpretation']} for more details).
• Figure 2: Model validation. (A) Mean velocity field $\bar{v}(x, y)$ at various locations $(x, y)$ in the station, visualized as flow lines along the field $\bar{v}$. The ellipsoids indicate the covariance matrix of the velocity vector at each location. (B) PDFs over simulated and observed vertical positions for various slices on the map in (A), indicated by the numbers ①-③. (C) PDF of the tortuosity of observed trajectories and trajectories simulated by the two model variants. The inset plot shows the autocorrelation function of the vertical velocity component. (D) Density of the relative position of the relative position of the nearest neighbor for observed and simulated data. For $T=0$, focusing on sample fidelity, the distribution of the relative position is more focused than for $T=0.1$.
• Figure 3: Understanding crowd physics by using NeCS for virtual surrogate experiments. (A) Sketches of experiments considered in this paper. We investigate the avoidance of pairs of pedestrians walking in opposite directions, the interactions of pedestrians walking in the same direction, and the strength of the force depending on the size and configuration of a static crowd in front of a pedestrian. The training data is analyzed to establish coverage of similar scenarios for each experiment, shown in the histograms. (B) Counterflow transfer function, depicting the lateral distance at the moment of passing $|\Delta y_s|$ as a function of the initial lateral distance $|\Delta y_i|$ between two pedestrians walking in opposite direction corbetta-pre-2018 Error bars indicate a single standard deviation. (C) Lateral force field for varying relative coordinates $\Delta x$, $\Delta y$ of a neighbor $j$ walking in opposite direction. Positive values (depicted in red) indicate repulsion, leading to avoidance. (D) Lateral force field as in C, but for a neighboring pedestrian $j$ walking in the same direction. The dashed line indicates the 0-interaction manifold, and the thick black line indicates an ellipsoid fit to this manifold. (E) Acceleration induced by interaction with a random crowd of varying size. Crowds consist of individuals with positions randomly selected from a lattice or sampled from a Gaussian distribution. The vertical dashed line indicates $N^* \approx 12$. (F) Acceleration resulting from interaction with a crowd with varying spacing. NeCS is compared to classical and top-$k$ social force model with and without vision constraint. Only a vision-driven top-$k$ force demonstrates a similar decay as NeCS.
• Figure 4: Generative model schematic.
• Figure 5: Schematic of model architecture.