Quantum-Inspired Modeling of Driving Behavior

Driver behavior is heterogeneous, context-dependent, and changes over time, and these properties shape the traffic phenomena we observe. Most models, however, fix in advance which behavioral variables interact and how. Behavior outside that form is absorbed as noise, while models flexible enough to capture it tend to lose interpretability. We introduce a quantum-inspired representation of driver behavior that combines properties usually treated separately or in part: it is continuous, probabilistic, context-dependent, history-dependent, and represents interactions among behavioral variables as learned from data. Each driver is encoded as an evolving density matrix, providing a unified representation of behavioral uncertainty, temporal evolution, and context-dependent behavioral variation. Trained without supervision on the I-24 MOTION dataset, the framework recovers three interpretable driving profiles representing three regimes: free flow, transition, and congestion. The profiles capture the behavioral range of the data and the smooth transitions drivers make between regimes as conditions change. The same representation also reproduces known macroscopic phenomena, aligning with the fundamental diagram and reproducing hysteresis loops. We also show how the representation supports practical use: it supplies context-dependent parameters to classical car-following models, and gives an autonomous vehicle a live behavioral read of the surrounding drivers with a short-horizon forecast of their motion. The framework points toward models of traffic that are interpretable and trustworthy by construction. We release an open-source toolkit on GitHub (https://github.com/mselayan/quantum-driver-representation) spanning data processing, training, inference, and analysis.

NOVA: Symbolic Regression Discovery of Interpretable Car-Following and Lane-Change Models with Driver Heterogeneity

We present NOVA, an autonomous symbolic regression framework that identifies interpretable car-following and lane-change structures from raw trajectory data with minimal behavioral priors. Applied to 4,765,788 active driving observations from the NGSIM I-80 and US-101 datasets, NOVA's deterministic Rust-powered search engine evaluates over 10,000 candidate algebraic structures and identifies a compact two-term acceleration model under a forward-shifted rolling-mean prediction target. Evaluated under two complementary preprocessing pipelines, NOVA achieves $RMSE = 1.376 m/s^2$ ($R^2 = 15.57\%$) on the intent-forecasting benchmark, outperforming the best recalibrated symbolic-regression baseline (SR-LLM, PNAS~2025) by 0.135 m/s$^2$ in RMSE under an identical evaluation protocol. Across eight independent experiments, a single dominant nonlinear term emerges as a robust backbone of human car-following; a residual-guided extension further links the selected structure to an established psychophysical theory of collision avoidance. The discovered feature operators transfer zero-shot between freeway sites with under 3 pp $R^2$ loss. Extended to lane-change modelling within a multinomial logit framework, NOVA achieves 67.4\% balanced accuracy under strict vehicle-ID holdout on 502 unseen drivers, surpassing existing lane-changing baselines by +29.8 percentage points on a three-class problem.