Traffic flow modeling relies heavily on fundamental diagrams. However, deterministic fundamental diagrams, such as single or multi-regime models, cannot capture the uncertainty pattern that underlies traffic flow. To address this limitation, a sparse non-parametric regression model is proposed in this paper to formulate the stochastic fundamental diagram. Unlike parametric stochastic fundamental diagram models, a non-parametric model is insensitive to parameters, flexible, and applicable. The computation complexity and the huge memory required for training in the Gaussian process regression have been reduced by introducing the sparse Gaussian process regression. The paper also discusses how empirical knowledge influences the modeling process. The paper analyzes the influence of modeling empirical knowledge in the prior of the stochastic fundamental diagram model and whether empirical knowledge can improve the robustness and accuracy of the proposed model. By introducing several well-known single-regime fundamental diagram models as the prior and testing the model's robustness and accuracy with different sampling methods given real-world data, the authors find that empirical knowledge can only benefit the model under small inducing samples given a relatively clean and large dataset. A pure data-driven approach is sufficient to estimate and describe the pattern of the density-speed relationship.

翻译：交通流建模严重依赖于基本图。然而，确定性基本图（如单区域或多区域模型）无法捕捉交通流中蕴含的不确定性模式。为解决这一局限，本文提出了一种稀疏非参数回归模型来构建随机基本图。与参数化随机基本图模型不同，非参数模型对参数不敏感、灵活且适用范围广。通过引入稀疏高斯过程回归，降低了高斯过程回归中训练所需的计算复杂度和巨大内存消耗。本文还探讨了经验知识如何影响建模过程。论文分析了随机基本图模型先验中建模经验知识的影响，以及经验知识能否提升所提模型的鲁棒性和准确性。通过引入几种经典的单区域基本图模型作为先验，并采用不同采样方法结合真实数据测试模型的鲁棒性和准确性，作者发现：仅当在相对干净且数据量较大的条件下采用少量诱导样本时，经验知识才能提升模型性能。纯数据驱动方法足以估计和描述密度-速度关系的模式。