Physics-informed deep learning with Kalman filter mixture for traffic state prediction

Accurate traffic forecasting is crucial for understanding and managing congestion for efficient transportation planning. However, conventional approaches often neglect epistemic uncertainty, which arises from incomplete knowledge across different spatiotemporal scales. This study addresses this challenge by introducing a novel methodology to establish dynamic spatiotemporal correlations that captures the unobserved heterogeneity in travel time through distinct peaks in probability density functions, guided by physics-based principles. We propose an innovative approach to modifying both prediction and correction steps of the Kalman filter (KF) algorithm by leveraging established spatiotemporal correlations. Central to our approach is the development of a novel deep learning (DL) model called the physics informed-graph convolutional gated recurrent neural network (PI-GRNN). Functioning as the state-space model within the KF, the PI-GRNN exploits established correlations to construct dynamic adjacency matrices that utilize the inherent structure and relationships within the transportation network to capture sequential patterns and dependencies over time. Furthermore, our methodology integrates insights gained from correlations into the correction step of the KF algorithm that helps in enhancing its correctional capabilities. This integrated approach proves instrumental in alleviating the inherent model drift associated with data-driven methods, as periodic corrections through update step of KF refine the predictions generated by the PI-GRNN. To the best of our knowledge, this study represents a pioneering effort in integrating DL and KF algorithms in this unique symbiotic manner. Through extensive experimentation with real-world traffic data, we demonstrate the superior performance of our model compared to the benchmark approaches.