The kinematics-based car-following models are usually applied in the longitudinal control of vehicles by mimicking drivers’ car-following maneuvers. However, due to the simplicity of the kinematics-based models, they are hard to accommodate the complex driving behaviors in real traffic. This paper proposes two models, namely GHR-BPNN and IDM-BPNN, which integrate a machine learning model, Back Propagation Neural Network(BPNN), with two kinematics-based car-following models, Gazis-Herman-Rothery(GHR) model and intelligent driver model(IDM), to improve the adaptiveness of the GHR and IDM for the complex real traffic. The two models take advantage of the self-learning capacity of the BPNN to improve the limited capacity of the GHR and the IDM on simulating complex driving behaviors owing to a few constant model parameters. Real vehicle trajectory data is used to calibrate the model parameters and test the model performances. Two evaluation indexes, i.e., the mean absolute error(MAE) and the mean absolute relative error(MARE), are selected for validating the model performance. The two models are expected to have a higher trajectory fitting accuracy than kinematics-based or machine learning-based car-following models individually. The findings of this paper could help us to understand how to improve the adaptiveness of the classical microscopic traffic flow model by utilizing machine learning tools. Keywords: car-following model, machine learning, Back Propagation Neural Network(BPNN), integrated model, microscopic traffic flow.

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