mlsanityData to 14 Oct 2026

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

arXiv 2508.03926 ↗First posted 5 Aug 2025cs.LG cs.NA math.DScited by 2

Not on the map. Why?

Abstract (arXiv)

Bridging the microscopic and macroscopic modelling scales in crowd dynamics constitutes an open challenge for systematic numerical analysis, optimization, and control. Here, we propose a manifold-informed machine learning approach to learn the discrete evolution operator for the emergent/collective crowd dynamics in latent spaces from high-fidelity individual/agent-based simulations. The proposed framework is a four-stage one, textitexplicitly 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 Kernel Density Estimation. In the second step, we construct a map from the density-field space into an appropriate latent space parametrized by a few coordinates based on Proper-Orthogonal Decomposition (POD) of the corresponding density distributions. The third step involves learning reduced-order surrogate models in the latent space using machine learning techniques, particularly Long Short-Term Memory networks and Multivariate Autoregressive models. Finally, we reconstruct the crowd dynamics in the high-dimensional space with POD, demonstrating that the POD reconstruction conserves the mass. Thus, with this ``embed -> learn in latent space -> lift back to the high-dimensional space'' pipeline, we create an effective solution operator of the unavailable (at the macroscopic scale) PDE for the evolution of the density distribution. For our illustrations, we used the Social Force Model to generate data in a corridor with an obstacle, imposing periodic boundary conditions in two scenarios: (i) a unidirectional flow, and (ii) a counterflow. The numerical results demonstrate high accuracy, robustness, and generalizability, thus allowing for fast and accurate modelling/simulation of crowd dynamics from agent-based simulations.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 34 of its 118 references that are in the map. First posted on arXiv 5 Aug 2025.

Builds on

34 of 118 references.

References · 34

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  3. 2019An Introduction to Variational Autoencoderscited by 1,000
  4. 2015Scheduled Sampling for Sequence Prediction with Recurrent Neural Networkscited by 803
  5. 2018Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networkscited by 690
  6. 2023GNOT: A General Neural Operator Transformer for Operator Learningcited by 336
  7. 2023Neural Operators for Accelerating Scientific Simulations and Designcited by 221
  8. 2022Physics-Informed Deep Neural Operator Networkscited by 113
  9. 2020Multiscale Simulations of Complex Systems by Learning their Effective Dynamicscited by 86
  10. 2017Numerical Gaussian Processes for Time-dependent and Non-linear Partial Differential Equationscited by 72
  11. 2021Learning effective stochastic differential equations from microscopic simulations: linking stochastic numerics to deep learningcited by 39
  12. 2019Coarse-scale PDEs from fine-scale observations via machine learningcited by 35
22 more
  1. 2024Transformers as Neural Operators for Solutions of Differential Equations with Finite Regularitycited by 34
  2. 2023AI-Aristotle: A Physics-Informed framework for Systems Biology Gray-Box Identificationcited by 29
  3. 2024RiemannONets: Interpretable Neural Operators for Riemann Problemscited by 28
  4. 2022Constructing coarse-scale bifurcation diagrams from spatio-temporal observations of microscopic simulations: A parsimonious machine learning approachcited by 25
  5. 2022Neural Integral Equationscited by 23
  6. 2020Pedestrian Trajectory Prediction with Convolutional Neural Networkscited by 21
  7. 2022Learning black- and gray-box chemotactic PDEs/closures from agent based Monte Carlo simulation datacited by 18
  8. 2022Data-driven Control of Agent-based Models: an Equation/Variable-free Machine Learning Approachcited by 15
  9. 2018Deep learning algorithm for data-driven simulation of noisy dynamical systemcited by 12
  10. 2021Deep learning via LSTM models for COVID-19 infection forecasting in Indiacited by 12
  11. 2023Interpretable learning of effective dynamics for multiscale systemscited by 11
  12. 2025Enabling Local Neural Operators to perform Equation-Free System-Level Analysiscited by 10
  13. 2024GoRINNs: Godunov-Riemann Informed Neural Networks for Learning Hyperbolic Conservation Lawscited by 8
  14. 2015Invisible control of self-organizing agents leaving unknown environmentscited by 7
  15. 2021Initializing LSTM internal states via manifold learningcited by 7
  16. 2021Time Series Forecasting Using Manifold Learningcited by 7
  17. 2020Principal component trajectories for modeling spectrally-continuous dynamics as forced linear systemscited by 5
  18. 2020Herding stochastic autonomous agents via local control rules and online global target selection strategiescited by 5
  19. 2023Data-driven modelling of brain activity using neural networks, Diffusion Maps, and the Koopman operatorcited by 5
  20. 2022Continuification-based control of large multiagent systems in a ringcited by 4
  21. 2014Modeling rationality to control self-organization of crowds: An environmental approachcited by 1
  22. 2019Mathematical models and methods for crowd dynamics controlcited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026RANDSMAPs: Random-Feature/multi-Scale Neural Decoders with Mass Preservationcited by 0
  2. 2026Physics-conforming Latent Twinscited by 0