Anatomy of Rollout Error in Chaotic Flow Surrogates

Autoregressive neural surrogates for turbulent PDEs are typically evaluated by rollout RMSE against a reference trajectory. However, in chaotic flows, trajectories often decorrelate due to sensitivity to initial conditions, making pointwise predic- tion errors meaningless. We investigate how surrogate errors develop and what aspects of the learned dynamics can still be evaluated beyond this predictability horizon. We compare deterministic and generative surrogates on 2D Kolmogorov flow using a shared backbone, focusing on models whose rollouts remain bounded. Our analysis reveals three findings. First, errors emerge at fine spatial scales before large-scale trajectory decorrelation. Second, despite trajectory divergence, local one-step errors measured against a numerical solver on model-generated states remain approximately constant with rollout depth. Third, one-step prediction ac- curacy does not necessarily translate into accurate long-term state statistics. This highlights the need to complement trajectory-based evaluation with measures of local dynamical accuracy and long-term statistical fidelity.