  We propose a kinematic wave based Deep Convolutional Neural Network (Deep
CNN) to estimate high resolution traffic speed dynamics from sparse probe
vehicle trajectories. To that end, we introduce two key approaches that allow
us to incorporate kinematic wave theory principles to improve the robustness of
existing learning-based estimation methods. First, we use an anisotropic
traffic-based kernel for the CNN. This kernel is designed to explicitly take
forward and backward traffic wave propagation characteristics into account
during reconstruction in the space-time domain. Second, we use simulated data
for training the CNN. This implicitly imposes physical constraints on the
patterns learned by the CNN, providing an alternate, unrestricted way to
integrate complex traffic behaviors into learning models. We present the speed
fields estimated using the anisotropic kernel and highlight its advantages over
its isotropic counterpart in terms of predicting shockwave dynamics.
Furthermore, we test the transferability of the trained model to real traffic
by using two datasets: the Next Generation Simulation (NGSIM) program and the
Highway Drone (HighD) dataset. Finally, we present an ensemble version of the
CNN that allows us to handle multiple (and unknown) probe vehicle penetration
rates. The results demonstrate that anisotropic kernels can reduce model
complexity while improving the correctness of the estimation, and that
simulation-based training is a viable alternative to model fitting using
real-world data. This suggests that exploiting prior traffic knowledge adds
value to learning-based estimation methods, and that there is great potential
in exploring broader approaches to do so.
