Physics-Informed Deep Learning with Kalman Filter Mixture: A New State Prediction Model

Harnessing a range of modeling approaches like Machine Learning (ML), Deep Learning (DL) etc. for analyzing spatiotemporal traffic data facilitates precise forecasts, optimizing transportation planning and congestion management for improved efficiency. Numerous studies in prediction modeling diligently incorporate spatiotemporal correlations into their analyses but fail to account for epistemic uncertainty which arises from incomplete knowledge across different spatiotemporal scales. This study aims to address this issue by capturing unobserved heterogeneity in travel time by considering distinct peaks in the probability density function, which we refer to as multimodal probability distribution while establishing causation through physics-based principles. The information obtained from this methodology is then employed in a new model called the Physics Informed-Graph Convolutional Gated Recurrent Neural Network (PI-GRNN). This DL model utilizes the inherent structure and relationships within the transportation network for capturing sequential patterns and dependencies in the data over time. The dynamic graph-based approach can utilize data from different locations and times to improve future travel time predictions at distant non-contiguous unobserved locations. We employ the PI-GRNN as the state-space model in the novel KF to obtain the evolution of the state with time. This approach will help in mitigating model drift caused by the data-driven approach by periodically correcting the PI-GRNN predictions with Kalman filter updates. To the best of our knowledge, this represents the pioneering data-driven multimodal multivariate learning approach to construct a dynamic graph of a traffic network. Furthermore, no other study has used the physics-informed data-driven technique as opposed to the mathematical model for the prediction step within the KF framework. Extensive experiments on real-world traffic data demonstrate that our model consistently outperforms the benchmark models.