A physics-informed deep learning paradigm for car-following models

•First-of-its-kind that employs a hybrid PIDL paradigm.•Leverage the advantage of both model-based and data-driven methods.•Demonstrate the superiority of PIDL using a comprehensive set of numerical experiments and NGSIM Car-following behavior has been extensively studied using physics-based models, such as Intelligent Driving Model (IDM). 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 model (PIDL-CF) architectures encoded with 4 popular physics-based models - the IDM, the Optimal Velocity Model, the Gazis-Herman-Rothery model, and the Full Velocity Difference Model. Acceleration is predicted for 4 traffic regimes: acceleration, deceleration, cruising, and emergency braking. The generalization of PIDL method is further validated using two representative neural network models: the artificial neural networks (ANN) and the long short-term memory (LSTM) model. Two types of PIDL-CF 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.