  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.
