Extreme-Scale Super-Resolution of Homogeneous Turbulence from a Single Realization

Homogeneous turbulent flows exhibit recurring multiscale structures across spatially separated regions, suggesting that a single flow realization may contain sufficient information to learn representations of unresolved scales. We investigate this hypothesis through an extreme super-resolution framework in which a wide-activation deep super-resolution (WDSR) network is trained exclusively on overlapping patches extracted from a single high-resolution turbulent realization. Previously unseen flow fields are reconstructed through patchwise prediction followed by Hann-window-weighted overlap-add assembly. The framework is evaluated for two-dimensional homogeneous isotropic turbulence at super-resolution factors of x32 and x64, representing severe spatial under-resolution. Despite the limited training data, the proposed approach reconstructs coherent vortical structures and recovers fine-scale features more accurately than conventional interpolation. Spectral and statistical analyses further demonstrate improved recovery of high-wavenumber energy content and multiscale flow characteristics. To assess the effectiveness of exploiting internal spatial information, we compare the proposed framework against WDSR models trained on 1, 25, 50, and 100 complete high-resolution snapshots without patch extraction. This comparison distinguishes the benefits of localized learning from those associated with increasing the number of training realizations. The results demonstrate that exploiting spatial redundancy within a single turbulent realization enables accurate reconstruction of previously unseen flow fields, even under extreme spatial under-resolution. These findings establish single-realization patch-based learning as a promising data-efficient approach for turbulent super-resolution when high-resolution training data are scarce.