A hybrid generative reduced-order model for the Minimal Flow Unit

Wall-bounded turbulent flows play a central role in engineering and geophysical applications. Most industrially relevant problems, however, are multi-query, requiring repeated evaluations of the flow that are too expensive for high-fidelity simulations. This article presents a data-driven surrogate model of wall-bounded turbulence that delivers long-horizon predictions from sparse measurements. The architecture couples a β -VAE-GAN, which compresses the flow fields into a compact latent manifold, with a sensor-conditioned Transformer that governs the latent dynamics. The model is evaluated on the wall-parallel plane at y + = 14 , where the turbulent kinetic energy peaks, in a Minimal Flow Unit at R e τ = 200 . On unseen test data, the β -VAE-GAN recovers 88% of the turbulent kinetic energy within a four-dimensional latent space, against 76% for a standard β -VAE. The latent coordinates separate the slow intermittency of the regeneration cycle from the streamwise convection of near-wall structures, while preserving the conditional interactions between the two, showing that the learnt representation retains the dynamical signature of the flow. From an initialisation window of 128 t + of encoded fields, the Transformer tracks the latent trajectories over 17,241 t + . When the predicted trajectories are decoded, the model recovers 82% of the turbulent kinetic energy. It also reproduces the pacing of alternating active and quiescent phases and the most frequent ejection and sweep events. These results present the framework as a step forward towards surrogate models for closed-loop flow control, parametric exploration and design optimisation, and raise new questions about what the learnt latent space reveals of the flow dynamics.