Discovering the optimal relationship hypothesis of car-following behaviors with neural network-based symbolic regression☆

Mathematical models describing the dynamics of traffic flow have become increasingly popular as tools supporting the analysis and evaluation of traffic systems. This paper focuses on microscopic simulation tools, specifically those employing ordinary differential equations (ODEs). In general, most ODEs-based traffic models (i.e., car-following models or CFMs for short) require prior behavioral assumptions, that is, the optimal traffic state relationships. These assumptions vary widely across traffic scenarios, posing limitations. To overcome this hurdle and enhance CFMs' practicability, this paper proposes a novel research paradigm-artificial intelligence (AI) for (traffic) physics or AI-driven traffic flow theory, to explore the mechanisms of car-following behaviors. The proposed neural network (SciNet)-based architecture for symbolic regression, called SciNet-CFM, can provide scientific hypotheses for the modeling of car-following behaviors from the AI perspective, thus relaxing the prior behavioral assumptions in current traffic theory. Specifically, symbolic regression is used to generate a tractable mathematical expression for CFM discovery, rather than the unexplained connection structure of traditional neural networks. The numerical and empirical experiments show that the SciNet-CFM has the potential to uncover the hidden properties of the observed microscopic traffic flow dynamics. The comparisons with classical and state-of-the-art models demonstrate a better performance of the proposed SciNet-CFM over traditional physics-based, data-driven, and hybrid models.