  We propose a kinematic wave-based Deep Convolutional Neural Network (Deep
CNN) to estimate high-resolution traffic speed fields from sparse probe vehicle
trajectories. 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 propose an anisotropic traffic
kernel for the Deep CNN. The anisotropic kernel explicitly accounts for
space-time correlations in macroscopic traffic and effectively reduces the
number of trainable parameters in the Deep CNN model. Second, we propose to use
simulated data for training the Deep CNN. Using a targeted simulated data for
training provides an implicit way to impose desirable traffic physical features
on the learning model. In the experiments, we highlight the benefits of using
anisotropic kernels and evaluate the transferability of the trained model to
real-world traffic using the Next Generation Simulation (NGSIM) and the German
Highway Drone (HighD) datasets. The results demonstrate that anisotropic
kernels significantly reduce model complexity and model over-fitting, and
improve the physical correctness of the estimated speed fields. We find that
model complexity scales linearly with problem size for anisotropic kernels
compared to quadratic scaling for isotropic kernels. Furthermore, evaluation on
real-world datasets shows acceptable performance, which establishes that
simulation-based training is a viable surrogate to learning from real-world
data. Finally, a comparison with standard estimation techniques shows the
superior estimation accuracy of the proposed method.
