Knowledge-data fusion oriented traffic state estimation: A stochastic physics-informed deep learning approach

• Stochastic physics-informed deep learning is proposed for traffic state estimation. • More realistic prior knowledge is fused to neural network frameworks to provide better boundaries. • Stochastic fundamental diagrams are adopted to capture the scattering effect. • Experiments results demonstrate the effectiveness of proposed SPIDL models. Physics-informed deep learning (PIDL)-based models have recently garnered remarkable success in Traffic State Estimation (TSE). However, the prior knowledge used to guide regularization training in current mainstream architectures is based on deterministic physical models. The drawback is that a solely deterministic model fails to capture the universally observed traffic flow dynamic scattering effect. Considering the existence of more realistic stochastic physical models that can reproduce the relationship between speed and flow, they can provide better bounds for neural network models with uncertainty. Therefore, this study, for the first time, incorporates stochastic physics information to improve the PIDL architecture and propose stochastic physics-informed deep learning (SPIDL) for traffic state estimation. The idea behind such SPIDL is simple and is based on the fact that a stochastic fundamental diagram provides the entire range of possible speeds for any given density with associated probabilities. Specifically, we select percentile-based fundamental diagram and distribution-based fundamental diagram as stochastic physics knowledge and design corresponding physics-uninformed neural networks for effective fusion, thereby realizing two specific SPIDL models, namely α -SPIDL and B -SPIDL. The main contribution of SPIDL lies in addressing the “overly centralized guidance” caused by the one-to-one speed-density relationship in deterministic models during neural network training, enabling the network to digest more reliable knowledge-based constraints. Experiments on real-world datasets indicate that proposed SPIDL models achieve accurate traffic state estimation in sparse data scenarios. More importantly, as expected, SPIDL models reproduce well the scattering effect of field observations, demonstrating the effectiveness of fusing stochastic physics model knowledge with deep learning frameworks.