Close one lane and the real-time demand calibration gets sharper: 63% lower density error than LimEKF on grid day 10

Real-time OD demand calibration no longer needs repeated simulator calls inside an iterative optimization; the prediction network and the simulator exchange information at every 5-minute step. Earlier online calibration relied mainly on general-purpose optimization and filtering, such as LimEKF, which replaces the online Kalman gain update with a fixed pre-computed gain matrix; such methods adapt poorly under congestion and sudden disruptions. In the 3×3 grid network, after link B1C1 closed at hour 4 on day 10, the framework reached a density MSE of 21.6 [veh/km]² against 57.9 [veh/km]² for LimEKF, a 63% reduction; over the first five adaptation days it was higher, 40.0 versus 29.4 [veh/km]².

Gradients need not pass through the non-differentiable microscopic simulator; they travel through a static traffic-assignment metamodel, and the gap between metamodel and simulator enters the loss as an error term. Microscopic simulators are black boxes and stochastic, so standard backpropagation cannot be applied directly; an existing alternative recasts calibration as adversarial distribution matching, which needs repeated simulation and is hard to run in real time. The metamodel relates demand to measured density through jam density, capacity, lane count and path travel times, and its computation scales linearly with network size; the same metamodel also drives offline pre-training that supplies initial parameters.

Network parameters take a single gradient-descent step per time interval, with gradient clipping to limit destabilizing updates from noisy density observations. Running several iterations per interval would cost proportionally more computation and would overfit the single noisy observation available at that step. The loss uses density rather than flow because the flow–density fundamental diagram is non-unique in flow, where one flow value can mean uncongested or congested traffic; density identifies the traffic state uniquely.

The demonstrated scope is two toy networks and the Tokyo expressway corridor: a 13.3 km two-lane road with six loop detectors and 27 OD pairs, with measurements aggregated every 5 minutes; the real dataset is restricted-access from the Tokyo Metropolitan Government and not publicly available.

The metamodel is static, so predictions degrade under oversaturated conditions and are corrected only gradually by online parameter updates; density measurements are noisier than flow, and sustained noise statistically indistinguishable from a genuine demand shift could still cause lasting bias. The prior-demand weight δ gives the lowest MSE at 0.001, performance is robust for δ ≤ 0.01, and systematic identification of the optimal δ is left for future work.