A Koopman-Theoretic Approach to Car-Following and Multi-Lane Interaction Modeling

This paper presents a Koopman operator-based approach for the car-following model using SwarmDMD, a dynamic mode decomposition (DMD)-type algorithm designed to capture multi-agent interactions. A central challenge in Koopman operator-based car-following dynamics modeling lies in selecting an appropriate dictionary of observable functions. While previous studies have demonstrated various techniques, including deep learning, to learn the Koopman operator, they do not yield analytical forms. To address this, we revisit classical physics-based car-following models and propose candidate observables inspired by their mathematical structures. These observables are used within the Koopman and DMD framework to reconstruct a follower’s acceleration. The corresponding speed and trajectory are then estimated from the reconstructed acceleration. We evaluate the framework using both simulated and real-world datasets, demonstrating strong potential for accuracy and interpretability. While this study focuses on single-lane human-driven vehicles (HDVs), the framework is easily extendable to multi-lane traffic and connected and autonomous vehicle (CAV) scenarios, highlighting its generality and versatility. We presented a comparative evaluation of the proposed model by contrasting its acceleration reconstruction performance with that of both physics-based and data-driven models. Additionally, we interpreted the individual entries of the SwarmDMD matrix by establishing their connections to parameters of physics-based models. The codes and data used in the paper are available at our GitHub page.