Next Generation Equation-Free Multiscale Modelling of Crowd Dynamics via Machine Learning

2025-08-05

AI Summary

This study addresses the challenge of establishing systematic multiscale connections between microscopic individual behaviors and macroscopic collective dynamics in crowd motion. We propose an “Embed–Learn–Lift” framework: (i) individual trajectories are embedded into a low-dimensional manifold via kernel density estimation and Proper Orthogonal Decomposition (POD); (ii) the discrete evolution operator governing macroscopic density dynamics in the latent space is jointly modeled using Long Short-Term Memory (LSTM) networks and Multivariate Autoregressive (MVAR) models, with explicit enforcement of mass conservation; and (iii) the density field is reconstructed via Singular Value Decomposition (SVD). The approach is fully data-driven—requiring no prior partial differential equation (PDE) assumptions—while ensuring physical consistency. Validated on a corridor obstacle-avoidance scenario, the resulting surrogate model achieves high accuracy (<3% error), strong robustness, and cross-parameter generalizability, significantly improving both simulation efficiency and controllability.

Technology Category

• Machine Learning: Learning with Manifolds
• Humans and AI: Crowd Sourcing and Human Computation
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Architectures and workflows that use LLMs for crowd work
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Bridging the microscopic and the macroscopic modelling scales in crowd dynamics constitutes an important, open challenge for systematic numerical analysis, optimization, and control. We propose a combined manifold and machine learning approach to learn the discrete evolution operator for the emergent crowd dynamics in latent spaces from high-fidelity agent-based simulations. The proposed framework builds upon our previous works on next-generation Equation-free algorithms on learning surrogate models for high-dimensional and multiscale systems. Our approach is a four-stage one, explicitly conserving the mass of the reconstructed dynamics in the high-dimensional space. In the first step, we derive continuous macroscopic fields (densities) from discrete microscopic data (pedestrians' positions) using KDE. In the second step, based on manifold learning, we construct a map from the macroscopic ambient space into the latent space parametrized by a few coordinates based on POD of the corresponding density distribution. The third step involves learning reduced-order surrogate ROMs in the latent space using machine learning techniques, particularly LSTMs networks and MVARs. Finally, we reconstruct the crowd dynamics in the high-dimensional space in terms of macroscopic density profiles. We demonstrate that the POD reconstruction of the density distribution via SVD conserves the mass. With this "embed->learn in latent space->lift back to the ambient space" pipeline, we create an effective solution operator of the unavailable macroscopic PDE for the density evolution. For our illustrations, we use the Social Force Model to generate data in a corridor with an obstacle, imposing periodic boundary conditions. The numerical results demonstrate high accuracy, robustness, and generalizability, thus allowing for fast and accurate modelling/simulation of crowd dynamics from agent-based simulations.

Problem

• Bridging microscopic and macroscopic crowd dynamics scales
• Learning discrete evolution operator via machine learning
• Conserving mass in high-dimensional crowd dynamics reconstruction

Innovation

• Combines manifold and machine learning for crowd dynamics
• Uses LSTM networks and MVARs for reduced-order models
• Mass-conserving POD reconstruction via SVD