Physics-informed deep learning for traffic state estimation based on the traffic flow model and computational graph method

Traffic state estimation (TSE) is a critical task for intelligent transportation systems. However, it is extremely challenging because the traffic data quality is often affected by the installation position of devices, data collection frequency, interference during the transmission process, etc, thus causing the problem of data sparsity or data missing. To address the issue of traffic state estimation under the scenario of data sparsity, we propose a TSE model that combines the computational graph with physics-informed deep learning (PIDL) methods. Firstly, we apply the computational graph method to determine the parameters of the traffic fundamental diagram. These parameters are embedded into the computational graph framework, and their values are determined through the forward propagation of variables and the backward propagation of errors. Next, we employ the PIDL method to realize TSE (taking the LWR model based on the Greenshields fundamental diagram as an example). The PIDL leverages the advantages of data-driven and model-driven approaches to achieve accurate traffic state estimation. Case studies are conducted using the NGSIM dataset under two sparse data scenarios: loop detectors and probe vehicles. Experimental results demonstrate that PIDL can accurately reconstruct the traffic state of the entire road segment based on partially observed data. Furthermore, compared to pure deep learning methods and other baseline models, PIDL performs better in situations with sparse data, thereby proving the feasibility of integrating domain knowledge with deep learning frameworks. This paper fully acknowledges the issue of data sparsity in TSE and effectively addresses it by applying the PIDL method to achieve precise TSE, which holds significant implications for the control and management of real traffic flow.