Traffic prediction by combining macroscopic models and Gaussian processes

Abstract

We propose a physics informed statistical framework for traffic travel time prediction. This combined approach has the merit to address the shortcomings of the purely model-driven or data-driven approaches, while leveraging their respective advantages. Indeed, models are based on physical laws, but cannot capture all the complexity of real phenomena. Plus they are rarely used for prediction since this requires future data such as boundary conditions. On the other hand, pure statistical outputs can violate basic characteristic dynamics in their prediction and do not reconstruct traffic conditions. Here, on one side, the discrepancy of the considered mathematical model with real data is represented by a Gaussian process. On the other side, the traffic simulator is fed with boundary data predicted by a Gaussian process, forced to satisfy the mathematical equations at virtual points, resulting in a multi-objective optimization problem. We validate our approach on both synthetic and real world data, showing that it delivers more reliable results compared to other methods.