Wrong Rays: In-Distribution Accuracy Does Not Certify Transport in Learned PDE Propagators

Neural PDE models are commonly evaluated by prediction error on held-out trajectories, but downstream physical tasks may depend on dynamical responses that are weakly constrained by this metric. We ask when in-distribution prediction accuracy certifies the transport of a localized disturbance. We find that low prediction error can coexist with systematically incorrect packet trajectories, or wrong rays, along spectral directions weakly weighted by the standard distribution, from an exact non-identifiability construction to trained models and released PDEBench data. We develop a task-conditioned characterization of this gap: the input distribution determines which operator directions are strongly constrained, whereas transport can be sensitive to different directions. In clean transport settings, this mismatch appears as phase-slope error that accumulates with rollout horizon; on released linear advection, phase-only correction accounts for \(81.7%\) of the improvement achieved by full-complex correction. The error is not removed by the tested representation-consistency, activation-anti-aliasing, or longer-training interventions. An information-presence test further shows that explicit spectral estimation recovers the corrective response from the same broadband observations that the tested end-to-end fine-tuning procedure fails to exploit reliably. These results distinguish predictive accuracy from certification of task-relevant dynamics.