Autoregressive rollout error in latent-space reduced-order models of bluff-body wakes is accumulated phase drift

Abstract

Autoregressive reduced order models suffer from compounding long horizon rollout errors, typically treated as unstructured noise. We demonstrate that for bluff body wakes across Re=100 to 800, this rollout error is highly structured and reveals what these models actually learn. For a convolutional autoencoder LSTM model, 95 % to 98% of the error is pure phase error, peaking sharply at the vortex shedding frequency. The network reproduces the attractor geometry almost exactly, matching limit cycle amplitudes within 0.15%, but traverses the cycle at slightly the wrong rate. This timing error, accumulating to just a few thousandths of a cycle over the entire rollout, drives the long horizon error even while one step validation errors appear virtually perfect. Because phase error drifts linearly, it can be corrected offline without retraining using just one parameter per latent coordinate, fitted on a short calibration window. The signal to noise ratio of this phase fit serves as a diagnostic that reliably predicts correction success (r=0.85 across 50 networks). While simple periodic baselines match this performance on stationary limit cycles, they fail by over an order of magnitude when applied to wakes driven by slowly varying inflows. Conversely, our phase correction requires only phase coherence, successfully removing roughly half of the rollout error during non stationary flow.