  Traffic state estimation (TSE), which reconstructs the traffic variables
(e.g., density) on road segments using partially observed data, plays an
important role on efficient traffic control and operation that intelligent
transportation systems (ITS) need to provide to people. Over decades, TSE
approaches bifurcate into two main categories, model-driven approaches and
data-driven approaches. However, each of them has limitations: the former
highly relies on existing physical traffic flow models, such as
Lighthill-Whitham-Richards (LWR) models, which may only capture limited
dynamics of real-world traffic, resulting in low-quality estimation, while the
latter requires massive data in order to perform accurate and generalizable
estimation. To mitigate the limitations, this paper introduces a
physics-informed deep learning (PIDL) framework to efficiently conduct
high-quality TSE with small amounts of observed data. PIDL contains both
model-driven and data-driven components, making possible the integration of the
strong points of both approaches while overcoming the shortcomings of either.
This paper focuses on highway TSE with observed data from loop detectors, using
traffic density as the traffic variables. We demonstrate the use of PIDL to
solve (with data from loop detectors) two popular physical traffic flow models,
i.e., Greenshields-based LWR and three-parameter-based LWR, and discover the
model parameters. We then evaluate the PIDL-based highway TSE using the Next
Generation SIMulation (NGSIM) dataset. The experimental results show the
advantages of the PIDL-based approach in terms of estimation accuracy and data
efficiency over advanced baseline TSE methods.
