Physics Priors Are Insurance: A Sign Change with Sensing Density in Traffic State Estimation

Physics-informed traffic state estimation imposes the Lighthill–Whitham–Richards conservation law on a network that reconstructs traffic density between roadside sensors, on the assumption that the physics can only help. On two shock-rich NGSIM corridors, against a strictly matched ablation and validation-tuned classical baselines (Treiber–Helbing adaptive smoothing, GP and $k$NN kriging), we find the term's effect changes sign with sensing density: with dense sensors the conservation-law residual makes reconstruction worse (+0.03–0.05 rel-$L^2$), and once 85–90% of sensors are withheld, removing it roughly doubles reconstruction error (0.65 vs. 0.34 at 90%, $p=0.002$, 10/10 paired seeds). A tuned classical smoother remains the strongest baseline at mid coverage; at the sparsest coverage physics is significantly best on US-101 and is statistically indistinguishable from the best classical method on I-80. A loss-conditional variant amortises the physics-weight search at $4.8\times$ lower compute.