发表机构
KTH; Trafikverket（皇家理工学院; 瑞典交通管理局）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究提出一种半参数随机基本图建模框架，利用特殊函数形式兼顾物理约束与复杂模式捕捉，推导矩匹配方程确保模型适定性，可扩展到非位置 - 尺度分布，实证表明其优于基线，为随机交通流建模提供理论基础和灵活框架。
AI 中文摘要
随机基本图（SFD）描述了交通密度与流量或速度之间的概率关系，有助于进行考虑不确定性的交通建模。然而，现有随机模型难以兼顾严格的物理约束和捕捉复杂非线性模式的灵活性。为此，我们提出一种新颖的半参数SFD建模框架，利用特殊设计的函数形式。这些函数内在地满足给定交通密度下条件流量分布矩的物理约束，同时结合基于神经网络的结构捕捉复杂经验模式。我们推导了矩匹配方程组将物理约束转化为条件分布参数化，证明位置 - 尺度分布族存在唯一解，确保模型适定性。还表明该框架可扩展到非位置 - 尺度分布。对真实数据集的实证评估显示，我们的方法始终优于代表性基线，在拥堵情况下概率精度更高且不确定性量化更稳健。总体而言，该框架为随机交通流建模提供了理论基础和灵活框架。
英文摘要
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.
Comments22 pages, 11 figures, 5 tables
