Generative super-resolution of turbulent flows via stochastic interpolants

Capturing the intricate multiscale features of turbulent flows remains a fundamental challenge due to the limited resolution of experimental data and the computational cost of high-fidelity simulations. In many practical scenarios only coarse representations of the flows are feasible, leaving crucial fine-scale dynamics unresolved. This study addresses that limitation by leveraging generative models to perform super-resolution of velocity fields and reconstruct the unresolved scales from low-resolution conditionals. In particular, the recently formalized stochastic interpolants are employed to super-resolve a case study of two-dimensional turbulence. Key to our approach is the iterative application of stochastic interpolants over local patches of the flow field, that enables efficient reconstruction without the need to process the full domain simultaneously. The patch-wise strategy is shown to yield physically consistent super-resolved flow snapshots, and key statistical quantities - such as the kinetic energy spectrum - are accurately recovered. Moreover, the patch-wise approach is observed to produce super-resolutions of a quality comparable to those produced using a full field approach, and, in general, stochastic interpolants are observed to outperform contesting generative models across a range of metrics. Although only demonstrated for a 2D case study, these results highlight the potential of using stochastic interpolants to super-resolve turbulent flows.