  Given the complexity and nonlinearity inherent in traffic dynamics within
vehicular platoons, there exists a critical need for a modeling methodology
with high accuracy while concurrently achieving physical analyzability.
Currently, there are two predominant approaches: the physics model-based
approach and the Artificial Intelligence (AI)--based approach. Knowing the
facts that the physical-based model usually lacks sufficient modeling accuracy
and potential function mismatches and the pure-AI-based method lacks
analyzability, this paper innovatively proposes an AI-based Koopman approach to
model the unknown nonlinear platoon dynamics harnessing the power of AI and
simultaneously maintain physical analyzability, with a particular focus on
periods of traffic oscillation. Specifically, this research first employs a
deep learning framework to generate the embedding function that lifts the
original space into the embedding space. Given the embedding space
descriptiveness, the platoon dynamics can be expressed as a linear dynamical
system founded by the Koopman theory. Based on that, the routine of linear
dynamical system analysis can be conducted on the learned traffic linear
dynamics in the embedding space. By that, the physical interpretability and
analyzability of model-based methods with the heightened precision inherent in
data-driven approaches can be synergized. Comparative experiments have been
conducted with existing modeling approaches, which suggests our method's
superiority in accuracy. Additionally, a phase plane analysis is performed,
further evidencing our approach's effectiveness in replicating the complex
dynamic patterns. Moreover, the proposed methodology is proven to feature the
capability of analyzing the stability, attesting to the physical analyzability.
