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.
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