Estimating motorway traffic states with data fusion and physics-informed deep learning

Traffic state estimation is an essential task in traffic engineering. It requires observations of traffic that are, so far, even with emerging technologies, only partially available at large, as neither Eulerian nor Lagrangian observations are available everywhere at all times. We propose a methodology to fuse both observation types using physics informed deep learning that is based on the Lighthill-Whitham-Richards (LWR) model to estimate traffic states at locations without observations, in particular to infer traffic density. We use two types of fundamental diagrams: Greenshields' parabola and a differentiable version of the trapezoidal fundamental diagram in the estimation. In the latter, we estimate from the observations the collective impact of all, even immeasurable, factors that lead to a reduction in traffic performance. We apply it to real-world data from the German motorway A9, where we find that it provides an opportunity to improve the estimation and understanding of traffic density by data fusion.