  A recent development in machine learning - physics-informed deep learning
(PIDL) - presents unique advantages in transportation applications such as
traffic state estimation. Consolidating the benefits of deep learning (DL) and
the governing physical equations, it shows the potential to complement
traditional sensing methods in obtaining traffic states. In this paper, we
first explain the conservation law from the traffic flow theory as ``physics'',
then present the architecture of a PIDL neural network and demonstrate its
effectiveness in learning traffic conditions of unobserved areas. In addition,
we also exhibit the data collection scenario using fog computing
infrastructure. A case study on estimating the vehicle velocity is presented
and the result shows that PIDL surpasses the performance of a regular DL neural
network with the same learning architecture, in terms of convergence time and
reconstruction accuracy. The encouraging results showcase the broad potential
of PIDL for real-time applications in transportation with a low amount of
training data.
