In this study, an equation-free method is used to perform bifurcation analyses of various artificial neural network (ANN) based car-following models. The ANN models were trained on Multiple Car Following (MCF) model output data (ANN-m) and field data (ANN-r). The ANN-m model could capture the behaviour of the MCF model in quite detail. A bifurcation analysis, using the circuit length $L$ as parameter, for the ANN-m model leads to good results if the training data set from the MCF model is sufficiently diverse, namely that it incorporates data from a wide range of vehicle densities that encompass the stable free-flow and the stable jam-flow regimes. The ANN-r model is in general able to capture the feature of traffic jams when a car takes headway and velocity of itself and of the two cars ahead as input. However, the traffic flow of the ANN-r model is more regular in comparison to the field data. It is possible to construct a partial bifurcation diagram in $L$ for the ANN-r using the equation-free method and it is found that the flow changes stability due to a subcritical Hopf bifurcation.

在本研究中，使用无方程方法对各种基于人工神经网络 (ANN) 的跟驰模型进行分岔分析。ANN 模型在多车跟随 (MCF) 模型输出数据 (ANN-m) 和现场数据 (ANN-r) 上进行了训练。ANN-m 模型可以非常详细地捕捉 MCF 模型的行为。分岔分析，使用电路长度$升$作为参数，如果来自 MCF 模型的训练数据集足够多样化，则 ANN-m 模型会产生良好的结果，即它包含来自广泛车辆密度的数据，包括稳定的自由流动和稳定的拥堵。流态。ANN-r 模型通常能够捕捉当一辆车以自身和前面两辆车的车头和速度作为输入时交通拥堵的特征。然而，与现场数据相比，ANN-r 模型的交通流更加规律。可以构造部分分叉图$升$ 对于使用无方程方法的 ANN-r，发现由于亚临界 Hopf 分叉，流动会改变稳定性。