When Context Is Not Enough: Modeling Unexplained Variability in Car-Following Behavior

TL;DR

This work addresses unexplained, context-driven variability in car-following by integrating a DeepAR-based mean model with a nonstationary Gaussian process residual governed by a scenario-adaptive Gibbs kernel. The approach learns context-dependent memory and uncertainty, enabling end-to-end probabilistic car-following simulations that better reproduce observed trajectories and provide sharper uncertainty estimates. Empirical results on the HighD dataset show that the nonstationary kernel yields superior RMSE, CRPS, and Energy Score across acceleration, speed, and spacing, outperforming stationary kernels and i.i.d. baselines, with ablations highlighting the importance of temporal correlations. The framework offers interpretable indicators of driving regimes and is practically applicable to uncertainty-aware microsimulation and safety-critical connected/autonomous vehicle analyses, with clear pathways for transferability and extension to more complex traffic scenarios.

Abstract

Modeling car-following behavior is fundamental to microscopic traffic simulation, yet traditional deterministic models often fail to capture the full extent of variability and unpredictability in human driving. While many modern approaches incorporate context-aware inputs (e.g., spacing, speed, relative speed), they frequently overlook structured stochasticity that arises from latent driver intentions, perception errors, and memory effects -- factors that are not directly observable from context alone. To fill the gap, this study introduces an interpretable stochastic modeling framework that captures not only context-dependent dynamics but also residual variability beyond what context can explain. Leveraging deep neural networks integrated with nonstationary Gaussian processes (GPs), our model employs a scenario-adaptive Gibbs kernel to learn dynamic temporal correlations in acceleration decisions, where the strength and duration of correlations between acceleration decisions evolve with the driving context. This formulation enables a principled, data-driven quantification of uncertainty in acceleration, speed, and spacing, grounded in both observable context and latent behavioral variability. Comprehensive experiments on the naturalistic vehicle trajectory dataset collected from the German highway, i.e., the HighD dataset, demonstrate that the proposed stochastic simulation method within this framework surpasses conventional methods in both predictive performance and interpretable uncertainty quantification. The integration of interpretability and accuracy makes this framework a promising tool for traffic analysis and safety-critical applications.

Figures (5)

• Figure 1: Traffic shockwave visualization of HighD dataset (Track #25, Lane #4), colored by speed (m/s).
• Figure 2: Joint and marginal distributions of the training‐set covariates along with the learned lengthscale. On the diagonal, the histograms show the empirical distribution of each variable: lengthscale $\ell$, gap $s$, relative speed $\Delta v$, speed $v$, and acceleration $a$. The off‐diagonal panels display bivariate contour estimates (kernel density plots) for each pair of variables, illustrating correlations between $\ell$ and the four car‐following covariates. In the top‐right corner, summary statistics are provided for reference.
• Figure 3: Simulated response of a 100-vehicle platoon to a smooth trapezoidal maneuver by the lead vehicle.
• Figure 4: Stochastic simulation results for three representative car-following cases. (a)-(c): Each example shows 100 predicted trajectories of spacing $s$, speed $v$, and acceleration $a$ (blue), compared to the ground-truth (black). The dashed line marks the forecast start. Below each example, simulated context-dependent $\ell(\boldsymbol{x}_t)$ and $\sigma(\boldsymbol{x}_t)$ (orange) are compared to DeepAR conditioned on ground truth (black). (d)-(f): Bottom-row heatmaps visualize the GP kernel $\boldsymbol{K}$, revealing the evolving temporal correlation structure during the forecast horizon.
• Figure 5: Error distributions under the DeepAR + Gibbs kernel (nonstationary GP) configuration over all test simulations. Each row corresponds to a different metric. Top: RMSE, middle: CRPS, bottom: ES. Each column corresponds to a different state (acceleration, speed, spacing). Histograms are normalized to percentage frequency; dashed vertical lines denote the mean values reported in \ref{['tab:models_comparison']}. Note the long tails in the spacing histograms, indicating that although the average gap error is low, extreme underestimations or overestimations can still occur.