Ludovic Leclercq

Eunhan Ka, Ludovic Leclercq, Satish V. Ukkusuri

Traffic state estimation from sparse fixed sensors is challenging because physics-informed neural networks (PINNs) tend to over-smooth the shockwaves admitted by the Lighthill-Whitham-Richards (LWR) model. This study proposes Adaptive Domain Decomposition Physics-Informed Neural Networks (ADD-PINN), a two-stage residual-guided framework for LWR-based offline speed-field reconstruction. A coarse global PINN is first trained; its spatial residual profile is then used to place subdomain boundaries and initialize child subnetworks in a decomposition-enabled mode, while a data-driven shock indicator can retain a single-domain fallback when localized evidence of transition is weak. The primary offline I-24 MOTION evaluation spans five days, five sensor configurations, and ten seeds per configuration, yielding 1,500 runs in total. Against neural and physics-informed baselines, ADD-PINN attains the lowest relative L2 error in 18 of 25 configurations and in 14 of 15 sparse-sensing cases, while training 2.4 times faster than the extended PINN (XPINN) baseline. An ablation study supports spatial-only decomposition as an effective default for fixed-sensor traffic reconstruction in the evaluated settings. Supplementary Next Generation Simulation (NGSIM) experiments serve as a negative control: the shock indicator suppresses decomposition in all 50 runs, and the default single-domain fallback ranks first across all sensor configurations. These results support residual-guided spatial decomposition as an effective PINN-family design for offline reconstruction when sparse fixed sensing coincides with localized transition regions.

Zhixiong Jin, Dimitrios Tsitsokas, Nikolas Geroliminis et al.

In large-scale traffic optimization, models based on Macroscopic Fundamental Diagram (MFD) are recognized for their efficiency in broad network analyses. However, they fail to reflect variations in the individual traffic status of each road link, leading to a gap in detailed traffic optimization and analysis. To address the limitation, this study introduces a Local Correction Factor (LCF) that represents local speed deviations between the actual link speed and the MFD average speed based on the link configuration. The LCF is calculated using a deep learning function that takes as inputs the average speed from the MFD and the road network configuration. Our framework integrates Graph Attention Networks (GATs) with Gated Recurrent Units (GRUs) to capture both the spatial configurations and temporal correlations within the network. Coupled with a strategic network partitioning method, our model enhances the precision of link-level traffic speed estimations while preserving the computational advantages of aggregate models. In our experiments, we evaluate the proposed LCF across various urban traffic scenarios, including different levels of origin-destination trip demand and distribution, as well as diverse road configurations. The results demonstrate the robust adaptability and effectiveness of the proposed model. Furthermore, we validate the practicality of our model by calculating the travel time of each randomly generated path, achieving an average error reduction of approximately 84% relative to MFD-based results.

Femke van Wageningen-Kessels, Ludovic Leclercq, Winnie Daamen et al.

A continuum crowd flow model is reformulated in the Lagrangian coordinate system. The system has proven to give computational advantages over the traditional Eulerian coordinate system for (one-dimensional) road traffic flow. Our extension of the model and simulation method to (two-dimensional) crowd flow paves the way to explore whether the advantages also hold in two dimensions. This paper provides a first exploration and shows that a model and simulation method for two-dimensional crowd flow can be developed in the Lagrangian coordinate system and that is leads to promising results.