When context is not enough: Modeling unexplained variability in car-following behavior

Modeling car-following behavior is fundamental to microscopic traffic simulation, yet even context-aware models can leave residual deviations whose magnitude and temporal persistence vary across driving conditions. This study introduces an interpretable stochastic framework that jointly represents the mean dynamics and the context-conditioned covariance of the residual process. The framework integrates deep neural networks with a nonstationary Gaussian process (GP) and employs a scenario-adaptive Gibbs kernel whose local lengthscale and amplitude evolve with the driving context. It thereby quantifies uncertainty in acceleration, speed, and spacing conditional on the selected inputs and mean model. Experiments on the naturalistic German-highway HighD dataset show that temporal correlation provides the main improvement over an i.i.d. residual. The Gibbs covariance yields further gains and provides local measures of residual persistence and magnitude. These properties make the framework useful for uncertainty-aware traffic simulation and provide a basis for safety-oriented evaluation. The code is publicly available at https://github.com/Chengyuan-Zhang/ISTTT26-When-Context-Is-Not-Enough .