Graph Surrogate Modeling for Closed-Loop Microscopic-Macroscopic Control of Mixed Traffic

We propose a graph neural surrogate framework that replaces the macroscopic partial differential equation solver inside a closed-loop mixed-autonomy traffic-control architecture, while preserving the coupling between scales. Microscopic human-driven and automated vehicle dynamics continuously reshape the macroscopic traffic field, and the predicted macroscopic state in turn informs the automated vehicle control law. We represent the macroscopic density and velocity state on a periodic ring-road graph and design a residual graph convolutional network that exploits spatial coupling between neighboring traffic cells through bidirectional message passing, capturing both downstream wave propagation and upstream shockwave formation. The surrogate is trained with a rollout-based objective to reduce the distribution shift between reference-driven training inputs and recursively generated states during closed-loop deployment, together with physics-informed conservation losses that anchor predictions to the governing traffic-flow structure. An outputspace interpolation mechanism extends the surrogate across the continuum of automation rates without retraining. Beyond openloop prediction accuracy, we evaluate whether the surrogate preserves macroscopic feedback fidelity, disturbance attenuation, and string-stable behavior once embedded in the closed loop. Results show that the surrogate achieves low prediction error that grows only gradually under extended recursive deployment, closely reproduces the feedback field and vehicle-level trajectories generated by the full solver-based controller, generalizes smoothly to unseen automation rates, and delivers a computational speedup of 4.35 times relative to the numerical reference solver, while preserving the disturbance-attenuation behavior of the underlying control framework.