  Car-following behavior has been extensively studied using physics-based
models, such as the Intelligent Driver Model. These models successfully
interpret traffic phenomena observed in the real-world but may not fully
capture the complex cognitive process of driving. Deep learning models, on the
other hand, have demonstrated their power in capturing observed traffic
phenomena but require a large amount of driving data to train. This paper aims
to develop a family of neural network based car-following models that are
informed by physics-based models, which leverage the advantage of both
physics-based (being data-efficient and interpretable) and deep learning based
(being generalizable) models. We design physics-informed deep learning
car-following (PIDL-CF) architectures encoded with two popular physics-based
models - IDM and OVM, on which acceleration is predicted for four traffic
regimes: acceleration, deceleration, cruising, and emergency braking. Two types
of PIDL-CFM problems are studied, one to predict acceleration only and the
other to jointly predict acceleration and discover model parameters. We also
demonstrate the superior performance of PIDL with the Next Generation
SIMulation (NGSIM) dataset over baselines, especially when the training data is
sparse. The results demonstrate the superior performance of neural networks
informed by physics over those without. The developed PIDL-CF framework holds
the potential for system identification of driving models and for the
development of driving-based controls for automated vehicles.
