The increasing adoption of electric vehicles (EVs) necessitates an understanding of their driving behavior to enhance traffic safety and develop smart driving systems. This study compares classical and machine learning models for EV car following behavior. Classical models include the Intelligent Driver Model (IDM), Optimum Velocity Model (OVM), Optimal Velocity Relative Velocity (OVRV), and a simplified CACC model, while the machine learning approach employs a Random Forest Regressor. Using a real world dataset of an EV following an internal combustion engine (ICE) vehicle under varied driving conditions, we calibrated classical model parameters by minimizing the RMSE between predictions and real data. The Random Forest model predicts acceleration using spacing, speed, and gap type as inputs. Results demonstrate the Random Forest's superior accuracy, achieving RMSEs of 0.0046 (medium gap), 0.0016 (long gap), and 0.0025 (extra long gap). Among physics based models, CACC performed best, with an RMSE of 2.67 for long gaps. These findings highlight the machine learning model's performance across all scenarios. Such models are valuable for simulating EV behavior and analyzing mixed autonomy traffic dynamics in EV integrated environments.

Internal combustion engine (ICE) vehicles and electric vehicles (EVs) exhibit distinct vehicle dynamics. EVs provide rapid acceleration, with electric motors producing peak power across a wider speed range, and achieve swift deceleration through regenerative braking. While existing microscopic models effectively capture the driving behavior of ICE vehicles, a modeling framework that accurately describes the unique car-following dynamics of EVs is lacking. Developing such a model is essential given the increasing presence of EVs in traffic, yet creating an easy-to-use and accurate analytical model remains challenging. To address these gaps, this study develops and validates a Phase-Aware AI (PAAI) car-following model specifically for EVs. The proposed model enhances traditional physics-based frameworks with an AI component that recognizes and adapts to different driving phases, such as rapid acceleration and regenerative braking. Using real-world trajectory data from vehicles equipped with adaptive cruise control (ACC), we conduct comprehensive simulations to validate the model's performance. The numerical results demonstrate that the PAAI model significantly improves prediction accuracy over traditional car-following models, providing an effective tool for accurately representing EV behavior in traffic simulations.

With the rapid development of automated vehicles (AVs) in recent years, commercially available AVs are increasingly demonstrating high-level automation capabilities. However, most existing AV safety evaluation methods are primarily designed for simple maneuvers such as car-following and lane-changing. While suitable for basic tests, these methods are insufficient for assessing high-level automation functions deployed in more complex environments. First, these methods typically use crash rate as the evaluation metric, whose accuracy heavily depends on the quality and completeness of naturalistic driving environment data used to estimate scenario probabilities. Such data is often difficult and expensive to collect. Second, when applied to diverse scenarios, these methods suffer from the curse of dimensionality, making large-scale evaluation computationally intractable. To address these challenges, this paper proposes a novel framework for full-scenario AV safety evaluation. A unified model is first introduced to standardize the representation of diverse driving scenarios. This modeling approach constrains the dimension of most scenarios to a regular highway setting with three lanes and six surrounding background vehicles, significantly reducing dimensionality. To further avoid the limitations of probability-based method, we propose a volume-based evaluation method that quantifies the proportion of risky scenarios within the entire scenario space. For car-following scenarios, we prove that the set of safe scenarios is convex under specific settings, enabling exact volume computation. Experimental results validate the effectiveness of the proposed volume-based method using both AV behavior models from existing literature and six production AV models calibrated from field-test trajectory data in the Ultra-AV dataset. Code and data will be made publicly available upon acceptance of this paper.

--A fundamental challenge in car-following modeling lies in accurately representing the multi-scale complexity of driving behaviors, particularly the intra-driver heterogeneity where a single driver's actions fluctuate dynamically under varying conditions. While existing models, both conventional and data-driven, address behavioral heterogeneity to some extent, they often emphasize inter-driver heterogeneity or rely on simplified assumptions, limiting their ability to capture the dynamic heterogeneity of a single driver under different driving conditions. T o address this gap, we propose a novel data-driven car-following framework that systematically embeds discrete driving regimes (e.g., steady-state following, acceleration, cruising) into vehicular motion predictions. Leveraging high-resolution traffic trajectory datasets, the proposed hybrid deep learning architecture combines Gated Recurrent Units for discrete driving regime classification with Long Short-T erm Memory networks for continuous kinematic prediction, unifying discrete decision-making processes and continuous vehicular dynamics to comprehensively represent inter-and intra-driver heterogeneity. Driving regimes are identified using a bottom-up segmentation algorithm and Dynamic Time Warping, ensuring robust characterization of behavioral states across diverse traffic scenarios. Comparative analyses demonstrate that the framework significantly reduces prediction errors for acceleration (maximum MSE improvement reached 58.47%), speed, and spacing metrics while reproducing critical traffic phenomena, such as stop-and-go wave propagation and oscillatory dynamics. Understanding and modeling car-following behavior is fundamental to microscopic traffic flow research, serving as a bridge between individual driving dynamics and macro-level traffic phenomena.

Physics-informed machine learning (PIML) is crucial in modern traffic flow modeling because it combines the benefits of both physics-based and data-driven approaches. In conventional PIML, physical information is typically incorporated by constructing a hybrid loss function that combines data-driven loss and physics loss through linear scalarization. The goal is to find a trade-off between these two objectives to improve the accuracy of model predictions. However, from a mathematical perspective, linear scalarization is limited to identifying only the convex region of the Pareto front, as it treats data-driven and physics losses as separate objectives. Given that most PIML loss functions are non-convex, linear scalarization restricts the achievable trade-off solutions. Moreover, tuning the weighting coefficients for the two loss components can be both time-consuming and computationally challenging. To address these limitations, this paper introduces a paradigm shift in PIML by reformulating the training process as a multi-objective optimization problem, treating data-driven loss and physics loss independently. We apply several multi-gradient descent algorithms (MGDAs), including traditional multi-gradient descent (TMGD) and dual cone gradient descent (DCGD), to explore the Pareto front in this multi-objective setting. These methods are evaluated on both macroscopic and microscopic traffic flow models. In the macroscopic case, MGDAs achieved comparable performance to traditional linear scalarization methods. Notably, in the microscopic case, MGDAs significantly outperformed their scalarization-based counterparts, demonstrating the advantages of a multi-objective optimization approach in complex PIML scenarios.

Ensuring safe and human-like trajectory planning for automated vehicles amidst real-world uncertainties remains a critical challenge. While existing car-following models often struggle to consistently provide rigorous safety proofs alongside human-like acceleration and deceleration patterns, we introduce a novel multi-phase projection-based car-following model. This model is designed to balance safety and performance by incorporating bounded acceleration and deceleration rates while emulating key human driving principles. Building upon a foundation of fundamental driving principles and a multi-phase dynamical systems analysis (detailed in Part 1 of this study \citep{jin2025WA20-02_Part1}), we first highlight the limitations of extending standard models like Newell's with simple bounded deceleration. Inspired by human drivers' anticipatory behavior, we mathematically define and analyze projected braking profiles for both leader and follower vehicles, establishing safety criteria and new phase definitions based on the projected braking lead-vehicle problem. The proposed parsimonious model combines an extended Newell's model for nominal driving with a new control law for scenarios requiring projected braking. Using speed-spacing phase plane analysis, we provide rigorous mathematical proofs of the model's adherence to defined safe and human-like driving principles, including collision-free operation, bounded deceleration, and acceptable safe stopping distance, under reasonable initial conditions. Numerical simulations validate the model's superior performance in achieving both safety and human-like braking profiles for the stationary lead-vehicle problem. Finally, we discuss the model's implications and future research directions.

Trajectory planning is essential for ensuring safe driving in the face of uncertainties related to communication, sensing, and dynamic factors such as weather, road conditions, policies, and other road users. Existing car-following models often lack rigorous safety proofs and the ability to replicate human-like driving behaviors consistently. This article applies multi-phase dynamical systems analysis to well-known car-following models to highlight the characteristics and limitations of existing approaches. We begin by formulating fundamental principles for safe and human-like car-following behaviors, which include zeroth-order principles for comfort and minimum jam spacings, first-order principles for speeds and time gaps, and second-order principles for comfort acceleration/deceleration bounds as well as braking profiles. From a set of these zeroth- and first-order principles, we derive Newell's simplified car-following model. Subsequently, we analyze phases within the speed-spacing plane for the stationary lead-vehicle problem in Newell's model and its extensions, which incorporate both bounded acceleration and deceleration. We then analyze the performance of the Intelligent Driver Model and the Gipps model. Through this analysis, we highlight the limitations of these models with respect to some of the aforementioned principles. Numerical simulations and empirical observations validate the theoretical insights. Finally, we discuss future research directions to further integrate safety, human-like behaviors, and vehicular automation in car-following models, which are addressed in Part 2 of this study \citep{jin2025WA20-02_Part2}, where we develop a novel multi-phase projection-based car-following model that addresses the limitations identified here.

Recently, artificial intelligence (AI)-enabled nonlinear vehicle platoon dynamics modeling plays a crucial role in predicting and optimizing the interactions between vehicles. Existing efforts lack the extraction and capture of vehicle behavior interaction features at the platoon scale. More importantly, maintaining high modeling accuracy without losing physical analyzability remains to be solved. To this end, this paper proposes a novel physics-encoded deep learning network, named PeMTFLN, to model the nonlinear vehicle platoon dynamics. Specifically, an analyzable parameters encoded computational graph (APeCG) is designed to guide the platoon to respond to the driving behavior of the lead vehicle while ensuring local stability. Besides, a multi-scale trajectory feature learning network (MTFLN) is constructed to capture platoon following patterns and infer the physical parameters required for APeCG from trajectory data. The human-driven vehicle trajectory datasets (HIGHSIM) were used to train the proposed PeMTFLN. The trajectories prediction experiments show that PeMTFLN exhibits superior compared to the baseline models in terms of predictive accuracy in speed and gap. The stability analysis result shows that the physical parameters in APeCG is able to reproduce the platoon stability in real-world condition. In simulation experiments, PeMTFLN performs low inference error in platoon trajectories generation. Moreover, PeMTFLN also accurately reproduces ground-truth safety statistics. The code of proposed PeMTFLN is open source.

Modeling car-following behavior is essential for traffic simulation, analyzing driving patterns, and understanding complex traffic flows with varying levels of autonomous vehicles. Traditional models like the Safe Distance Model and Intelligent Driver Model (IDM) require precise parameter calibration and often lack generality due to simplified assumptions about driver behavior. While machine learning and deep learning methods capture complex patterns, they require large labeled datasets. Foundation models provide a more efficient alternative. Pre-trained on vast, diverse time series datasets, they can be applied directly to various tasks without the need for extensive re-training. These models generalize well across domains, and with minimal fine-tuning, they can be adapted to specific tasks like car-following behavior prediction. In this paper, we apply Chronos, a state-of-the-art public time series foundation model, to analyze car-following behavior using the Open ACC dataset. Without fine-tuning, Chronos outperforms traditional models like IDM and Exponential smoothing with trend and seasonality (ETS), and achieves similar results to deep learning models such as DeepAR and TFT, with an RMSE of 0.60. After fine-tuning, Chronos reduces the error to an RMSE of 0.53, representing a 33.75% improvement over IDM and a 12-37% reduction compared to machine learning models like ETS and deep learning models including DeepAR, WaveNet, and TFT. This demonstrates the potential of foundation models to significantly advance transportation research, offering a scalable, adaptable, and highly accurate approach to predicting and simulating car-following behaviors.

Microscopic traffic simulations are used to evaluate the impact of infrastructure modifications and evolving vehicle technologies, such as connected and automated driving. Simulated vehicles are controlled via car-following, lane-changing and junction models, which are designed to imitate human driving behavior. However, physics-based car-following models (CFMs) cannot fully replicate measured vehicle trajectories. Therefore, we present model extensions for the Intelligent Driver Model (IDM), of which some are already included in the Extended Intelligent Driver Model (EIDM), to improve calibration and validation results. They consist of equations based on vehicle dynamics and drive off procedures. In addition, parameter selection plays a decisive role. Thus, we introduce a framework to calibrate CFMs using drone data captured at a signalized intersection in Stuttgart, Germany. We compare the calibration error of the Krauss Model with the IDM and EIDM. In this setup, the EIDM achieves a 17.78 % lower mean error than the IDM, based on the distance difference between real world and simulated vehicles. Adding vehicle dynamics equations to the EIDM further improves the results by an additional 18.97 %. The calibrated vehicle-driver combinations are then investigated by simulating the traffic in three different scenarios: at the original intersection, in a closed loop and in a stop-and-go wave. The data shows that the improved calibration process of individual vehicles, openly available at https://www.github.com/stepeos/pycarmodel_calibration, also provides more accurate macroscopic results.