Physics-Informed Deep Learning for Traffic State Estimation on Freeways: A Comprehensive Comparative Study

Traffic state estimation (TSE) lays the foundation for freeway traffic monitoring and control. This paper develops a novel freeway traffic state estimator based on physics-informed deep learning (PIDL), whereby the deep-learning neural network is guided with physical laws of traffic. The innovative features of this work are as follows. In the data-driven aspect, the representation capability of neural networks is enhanced by introducing a nonlinear expansion layer, an attention mechanism, and a point-weighting mechanism. In traffic flow modeling aspect, a neural network is designed for the adaptive identification of model parameters. Additionally, a ramp flow self-learning neural network is constructed in consideration of system observability. This study employs four macroscopic traffic flow models LWR, ARZ, JWZ and PW to design PIDL-based traffic state estimators. Field-data evaluations and comparative analyses are conducted with respect to an urban expressway of 17.5 km. The results show that the designed PIDL traffic state estimators are able to simultaneously achieve traffic state estimation, ramp flow estimation, and adaptive identification of model parameters. The PIDL estimators outperform a number of baseline estimators, and are least sensitive to the number of input sensors and missing data. It is also discovered that the effectiveness of PIDL hinges on the appropriate tuning of the imbedded physical model as well as accurate boundary condition inputs, and failure to meet these requirements may lead to performance degradation.