AI summaryⓘ
The authors address the problem of estimating traffic conditions from limited sensor data, which is hard because traditional physics-based neural networks often smooth out sudden changes in traffic flow. They propose a new two-step method called ADD-PINN that first learns a rough global traffic pattern and then breaks the area into smaller parts for better detailed learning, using clues from the first step to decide where to split. Their approach works better and faster than previous methods in most tested cases with limited sensors, especially when sudden traffic changes occur. However, in simulations without sharp traffic changes, sticking to a single model works best, confirming their method's strength lies in handling localized transitions.
Traffic state estimationPhysics-informed neural networks (PINNs)Lighthill-Whitham-Richards (LWR) modelShockwavesDomain decompositionResidual-guided learningSparse sensingSpeed-field reconstructionI-24 MOTION datasetNGSIM
Authors
Eunhan Ka, Ludovic Leclercq, Satish V. Ukkusuri
Abstract
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.