Anatomy of Rollout Error in Chaotic Flow Surrogates

Autoregressive neural surrogates for turbulent PDEs are typically evaluated by rollout RMSE against a reference trajectory. In chaotic flows two trajectories decorrelate at a rate set by the Lyapunov exponent, so pointwise tracking says little at long horizons. We study what remains, comparing deterministic and generative surrogates on 2D Kolmogorov flow under a shared backbone, in the regime where rollouts stay bounded. In the Fourier domain, decorrelation sets in well before the chaos floor, driven by fine-scale errors present from the first step. Past that horizon we separate local dynamical error, measured against a solver on the model's own states, from the distance between generated and physical state distributions. The local error stays flat with rollout depth, yet the model with the lowest one is among the worst on the distribution it produces.