Distance-informed Neural Eikonal Solver for reactive dynamic user-equilibrium of macroscopic continuum traffic flow model
Date:
Ye, Y.*, Liang, H., Sun, J., & Chen, X. (2024, December 9-10). Distance-informed Neural Eikonal Solver for reactive dynamic user-equilibrium of macroscopic continuum traffic flow model [Poster Presentation]. The 28th International Conference of Hong Kong Society for Transportation Studies, Hong Kong, China.
Abstract: This paper revisits the Reactive Dynamic User-Equilibrium (RDUE) model for dynamic traffic assignment (DTA) of macroscopic traffic flow in two-dimensional continuum space, focusing on the Eikonal equation—a crucial partial differential equation (PDE) with specific boundary conditions. Traditionally, solving Eikonal equations has relied on iterative numerical methods through the discretization of the continuum space. However, this discretization compromises the precision of numerical solutions and could lead to non-convergence issues during iterative processes. This study refers to Physics-Informed Neural Networks (PINNs) and develops the Distance-Informed Neural Eikonal Solver (NES-DI) for solving Reactive Dynamic User-Equilibrium models. While the previously proposed Neural Eikonal Solver (NES) performs badly in a strong heterogeneous cost field with large cost differences, NES-DI explicitly considers the influence of solid boundaries during the factorization process by incorporating distance information. In the numerical example, the DTA problem, which predicts the route choices in continuum urban areas, demonstrates that under the mesh size of 1001x1001, NES-DI achieves a reduction of over 62% in the relative mean absolute error compared to the first-order fast sweeping method and over 86% compared to NES. Furthermore, NES-DI addresses the discretization issue, facilitating predictions of solutions at arbitrary locations within the computation domain. The NES-DI shows the potential of solving RDUE problems with strong heterogeneity, which offers a promising alternative to discretization-reliant numerical methods.