Neural operators struggle to learn complex PDEs in pedestrian mobility: Hughes model case study

This paper investigates the limitations of neural operators in learning solutions for a Hughes model, a first-order hyperbolic conservation law system for crowd dynamics. The model couples a Fokker-Planck equation representing pedestrian density with a Hamilton-Jacobi-type (eikonal) equation. This Hughes model belongs to the class of nonlinear hyperbolic systems that often exhibit complex solution structures, including shocks and discontinuities. In this study, we assess the performance of three state-of-the-art neural operators (Fourier Neural Operator, Wavelet Neural Operator, and Multiwavelet Neural Operator) in various challenging scenarios. Specifically, we consider (1) discontinuous and Gaussian initial conditions and (2) diverse boundary conditions, while also examining the impact of different numerical schemes.

@article{chauhan2025_2504.18267,
  title={ Neural operators struggle to learn complex PDEs in pedestrian mobility: Hughes model case study },
  author={ Prajwal Chauhan and Salah Eddine Choutri and Mohamed Ghattassi and Nader Masmoudi and Saif Eddin Jabari },
  journal={arXiv preprint arXiv:2504.18267},
  year={ 2025 }
}