A Semiparametric Framework for Stochastic Fundamental Diagram Modeling
Machine Learning
Summary
The authors developed a new way to model how traffic flow relates to traffic density while including randomness and uncertainty. Their method uses special mathematical functions combined with neural networks to make sure the model follows real physical rules and can still learn complex traffic patterns. They proved their model is stable and can work with different types of probability distributions. Tests on real traffic data showed their approach is more accurate and reliable than previous models, especially when traffic is heavy. Overall, their work offers a solid and flexible method for predicting traffic behavior with uncertainty.
Authors
Pengnan Chi, Xiaoliang Ma, Magnus Jansson, Magnus Nordenvaad
Abstract
The stochastic fundamental diagram (SFD) provides a probabilistic description of the relationship between traffic density and flow or speed, enabling uncertainty-aware traffic modeling. However, existing stochastic models frequently struggle to accommodate rigorous physical constraints while retaining sufficient flexibility to capture complex nonlinear patterns. To address this, we propose a novel semiparametric SFD modeling framework by leveraging specially designed functional forms. These functions intrinsically satisfy physical constraints defined on the moments of the conditional flow distribution given traffic density while incorporating neural-network-based structures to capture complex empirical patterns. We derive a system of moment-matching equations to convert physical constraints into the parameterization of the conditional distribution, proving that a unique solution exists for the location-scale family of distributions, thereby guaranteeing model well-posedness. Furthermore, we demonstrate that the framework can be extended to non-location-scale distributions, including those requiring additional boundary constraints. Empirical evaluations on a real-world dataset reveal that our approach consistently outperforms representative baselines, delivering superior probabilistic accuracy and robust uncertainty quantification, particularly in congested regimes. Overall, the proposed framework provides a theoretically grounded and flexible foundation for stochastic traffic flow modeling.