Physics-Informed Deep Learning Framework for Urban Traffic Network State Data Imputation

Traffic state is the foundation of urban transportation system management and operation, requiring a substantial amount of spatiotemporal traffic data. However, because of the limitations of data collection devices and recording technologies, traffic state missing-data problems are inevitable. To address this issue, this study proposes a hybrid framework MFD-TGCN (Macroscopic Fundamental Diagram-Temporal Graph Convolution Network) for traffic state imputation, based on the structure of physics-informed deep learning (PIDL). This framework integrates the strengths of physics-based traffic flow models and data-driven models for spatiotemporal feature dependency. To accommodate the physical features of various traffic state scenarios, three alternative Macroscopic Fundamental Diagram (MFD) models are utilized, and the Weighted Least Square (WLS) algorithm is applied for the initial parameter calibration. Meanwhile, the Graph Convolutional Network (GCN) and Gated Recurrent Unit (GRU) modules are employed effectively to capture the spatiotemporal features. The framework’s performance is evaluated using real-world traffic flow and density data from Chongqing, China, under different missing-data patterns, missing-data ratios, and varying numbers of network detectors, comparing with several categories of baseline methods. The results demonstrate that incorporating the road network information helps capture more spatial features, enhancing the accuracy of traffic network state imputation. The results confirm the superior performances of our framework over state-of-the-art methods in various scenarios, especially in cases with significant and complex missing data. Furthermore, experimental evidence indicates the combined physics and data-driven models framework has great generalizability capability for flexible scenarios in transportation system planning, management and control.