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.

Recent endeavors aimed at forecasting future traffic flow states through deep learning encounter various challenges and yield diverse outcomes. A notable obstacle arises from the substantial data requirements of deep learning models, a resource often scarce in traffic flow systems. Despite the abundance of domain knowledge concerning traffic flow dynamics, prevailing deep learning methodologies frequently fail to fully exploit it. To address these issues, we propose an innovative solution that merges Convolutional Neural Networks (CNNs) with Long Short-Term Memory (LSTM) architecture to enhance the prediction of traffic flow dynamics. A key revelation of our research is the feasibility of sampling training data for large traffic systems from simulations conducted on smaller traffic systems. This insight suggests the potential for referencing a macroscopic-level distribution to inform the sampling of microscopic data. Such sampling is facilitated by the observed scale invariance in the normalized energy distribution of the statistical mechanics model, thereby streamlining the data generation process for large-scale traffic systems. Our simulations demonstrate promising agreement between predicted and actual traffic flow dynamics, underscoring the efficacy of our proposed approach.