On the stochastic representation of a physics–data hybrid driven car-following model framework

Data-driven car-following models based on machine learning have demonstrated superior performance in microscopic trajectory prediction compared with traditional deterministic models. However, real-world transportation systems are complex and exhibit rich macroscopic phenomena such as traffic oscillations, stop-and-go waves and the concave growth of speed variance along vehicle platoons. Models that only fit microscopic data well often fail to replicate these emergent macroscopic features. This paper investigates stochastic modeling within a physics-informed, data-driven car-following framework. Using field experimental data collected in Hefei, we first compare a typical deep learning car-following model with a physics-informed data-driven model that embeds physical driving mechanisms. We evaluate their performance in reproducing macroscopic traffic characteristics and identify their limitations. The results show that directly embedding deterministic physical models primarily improves microscopic prediction accuracy but has limited impact on reproducing macroscopic oscillations. To address this issue, we introduce stochastic elements into the physics-informed deep learning model. By incorporating controlled randomness at the model output level, we significantly enhance the model’s ability to reproduce traffic oscillations and the concave growth pattern of speed standard deviation. Furthermore, we design a deep learning architecture with a trainable noise layer, enabling simultaneous calibration of model and noise parameters in a data-driven manner. This architecture achieves a better balance between microscopic accuracy and macroscopic fidelity. Our findings highlight the crucial role of stochasticity in capturing the complexity and uncertainty of traffic flow. The proposed physics-informed, stochastic, data-driven framework provides a promising direction for improving the realism and robustness of traffic flow simulations.