Capturing the equilibrium traffic state hypothesis of car-following models with artificial neural network

Mathematical models describing traffic flow dynamics have become increasingly popular as tools for analyzing and evaluating traffic systems. Different tools and methods are used to model and simulate complex traffic systems. Depending on their application purposes, macroscopic simulation tools use a set of partial differential equations (PDEs), while microscopic simulation tools are based on a set of ordinary differential equations (ODEs). In this study, the focus is on ODEs, which describe the motion of each vehicle in the system using the car-following theory. Traditionally, the car-following model in ODEs assumes an equilibrium speed function (or equilibrium headway function in some specific models). However, this assumption is not always accurate, as the parameters of the equilibrium function vary widely under different traffic conditions. Consequently, most models have advantages in the performance of different scenarios, and none can replace the other models. To address this issue, this paper proposes a novel approach that relaxes the essential assumption of the car-following model used in ODEs. The proposed framework can establish an interpretable car-following model and obtain formulaic modeling hypotheses of the equilibrium function. This approach can serve as an emerging paradigm for microscopic traffic flow modeling.