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：交通流建模在很大程度上依赖于基本图。然而，确定性基本图，例如单区域或多区域模型，无法捕捉交通流所固有的不确定性模式。为应对这一局限，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，且具有灵活性和适用性。通过引入稀疏高斯过程回归，降低了高斯过程回归在训练时所需的计算复杂度和巨大内存需求。本文还探讨了经验知识如何影响建模过程。文章分析了在随机基本图模型先验中引入经验知识的影响，以及经验知识是否能提高所提模型的鲁棒性和准确性。通过引入几种著名的单区域基本图模型作为先验，并利用真实世界数据通过不同采样方法测试模型的鲁棒性和准确性，作者发现，在给定相对干净且大规模数据集的情况下，经验知识仅在小规模诱导样本下对模型有益。纯数据驱动的方法足以估计和描述密度-速度关系的模式。