Generative Super-Resolution of Turbulent Flows via Stochastic Interpolants

TL;DR

This paper introduces a novel method using stochastic interpolants for super-resolving turbulent flow fields from low-resolution data, effectively capturing fine-scale dynamics with high physical fidelity.

Contribution

It demonstrates the application of stochastic interpolants to turbulence super-resolution, employing a patch-wise approach for efficient and accurate reconstruction of flow features.

Findings

Accurately recovers kinetic energy spectrum and dissipation rate.

Outperforms other generative models in quality metrics.

Enables physically consistent super-resolved flow snapshots.

Abstract

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 and the spatially averaged dissipation rate -- are accurately recovered. Moreover, compared with full-field reconstruction, the patch-wise approach produces higher-quality super-resolutions, and, in general, stochastic interpolants are observed to outperform contesting generative models across a range of metrics. These results establish stochastic interpolants as a viable tool for super-resolving turbulent flows and highlight their potential for future applications.