  This paper aims to quantify uncertainty in traffic state estimation (TSE)
using the generative adversarial network based physics-informed deep learning
(PIDL). The uncertainty of the focus arises from fundamental diagrams, in other
words, the mapping from traffic density to velocity. To quantify uncertainty
for the TSE problem is to characterize the robustness of predicted traffic
states. Since its inception, generative adversarial networks (GAN) have become
a popular probabilistic machine learning framework. In this paper, we will
inform the GAN based predictions using stochastic traffic flow models and
develop a GAN based PIDL framework for TSE, named ``PhysGAN-TSE". By conducting
experiments on a real-world dataset, the Next Generation SIMulation (NGSIM)
dataset, this method is shown to be more robust for uncertainty quantification
than the pure GAN model or pure traffic flow models. Two physics models, the
Lighthill-Whitham-Richards (LWR) and the Aw-Rascle-Zhang (ARZ) models, are
compared as the physics components for the PhysGAN, and results show that the
ARZ-based PhysGAN achieves a better performance than the LWR-based one.
