A Physics-informed Deep Operator for Real-Time Freeway Traffic State Estimation

Traffic state estimation (TSE) falls methodologically into three categories: model-driven, data-driven, and model-data dual-driven. Model-driven TSE relies on macroscopic traffic flow models originated from hydrodynamics. Data-driven TSE leverages historical sensing data and employs statistical models or machine learning methods to infer traffic state. Model-data dual-driven traffic state estimation attempts to harness the strengths of both aspects to achieve more accurate TSE. From the perspective of mathematical operator theory, TSE can be viewed as a type of operator that maps available measurements of inerested traffic state into unmeasured traffic state variables in real time. For the first time this paper proposes to study real-time freeway TSE in the idea of physics-informed deep operator network (PI-DeepONet), which is an operator-oriented architecture embedding traffic flow models based on deep neural networks. The paper has developed an extended architecture from the original PI-DeepONet. The extended architecture is featured with: (1) the acceptance of 2-D data input so as to support CNN-based computations; (2) the introduction of a nonlinear expansion layer, an attention mechanism, and a MIMO mechanism; (3) dedicated neural network design for adaptive identification of traffic flow model parameters. A traffic state estimator built on the basis of this extended PI-DeepONet architecture was evaluated with respect to a short freeway stretch of NGSIM and a large-scale urban expressway in China, along with other four baseline TSE methods. The evaluation results demonstrated that this novel TSE method outperformed the baseline methods with high-precision estimation results of flow and mean speed.