Generalizable super-resolution turbulence reconstruction from minimal training data

TL;DR

SoZoGAN addresses the challenge of generalizing turbulence super-resolution across diverse flows without retraining by exploiting the universality of small-scale motions from Kolmogorov $K41$ theory. It builds a library of scale-indexed SRGANs pretrained on HIT, then uses a physics-guided zonal decomposition and a mesoscale-to-microscale estimator (MLP) to perform zero-shot, locally matched super-resolution in inhomogeneous flows. The approach yields high-fidelity reconstructions in HIT, turbulent boundary layers, and channel flow, with robust performance up to moderate super-resolution factors and demonstrated resilience to partitioning choices. This framework reduces data requirements, maintains physical fidelity through a continuity constraint, and is architecture-agnostic, enabling broad applicability in industrial and natural turbulence contexts.

Abstract

Fully resolving turbulent flows remains challenging due to turbulent systems' multiscale complexity. Existing data-driven approaches typically demand expensive retraining for each flow scenario and struggle to generalize beyond their training conditions. Leveraging the universality of small-scale turbulent motions (Kolmogorov's K41 theory), we propose a Scale-oriented Zonal Generative Adversarial Network (SoZoGAN) framework for high-fidelity, zero-shot turbulence generation across diverse domains. Unlike conventional methods, SoZoGAN is trained exclusively on a single dataset of moderate-Reynolds-number homogeneous isotropic turbulence (HIT). The framework employs a zonal decomposition strategy, partitioning turbulent snapshots into subdomains based on scale-sensitive physical quantities. Within each subdomain, turbulence is synthesized using scale-indexed models pre-trained solely on the HIT database. SoZoGAN demonstrates high accuracy, cross-domain generalizability, and robustness in zero-shot super-resolution of unsteady flows, as validated on untrained HIT, turbulent boundary layer, and channel flow. Its strong generalization, demonstrated for homogenous and inhomogenous turbulence cases, suggests potential applicability to a wider range of industrial and natural turbulent flows. The scale-oriented zonal framework is architecture-agnostic, readily extending beyond GANs to other deep learning models.

Figures (16)

• Figure 1: The SoZoGAN framework for turbulence super-resolution that generalizes across diverse turbulent flows using "zero-shot" transfer. (a) Establishment of a pretrained super-resolution model library using a single dataset. (b) Zonal decomposition and microscale estimation based on the low-resolution flow field. (c) Microscale alignments of the decomposed subdomains and the procedure of "zero-shot" generation from low-resolution subdomains to the super-resolution global flow field. (d) Test cases of the proposed framework, including HIT, turbulent boundary layer and channel flow.
• Figure 2: Data curation from a single HIT dataset and verification of the scaling transformation method: (a) Schematic of the spatial and temporal sampling procedure to obtain initial planes, followed by (b) extension into velocity sub-planes. Scaling transformation is applied to extract sub-plane samples with different microscales from the initial planes. The numbers labeled in the top-right corner of each sub-plane ($\gamma$) represent the scaling ratios in the $x$ or $y$ direction relative to the width or height of the initial plane. (c) Validity of the scaling transformation. The scaling ratios $\gamma$ and the Taylor microscales $\lambda'_{\gamma}$ are nearly in a linear relationship for a series of HIT sub-planes.
• Figure 3: Effect of training-testing scale alignment on small-scale HIT generations with SoZoGAN. (a) Low-resolution ($1/5 \times$) input field for the $v$-velocity component. (b)-(d) Instantaneous $v$-component fields generated by SRGANs trained at different Taylor microscales: (b) training scale much larger than testing, (c) testing scale much larger than training, (d) matched scales, compared with (e) high-resolution reference fields. Taylor microscales $\lambda_{\text{LR}}$, $\lambda_{\text{SR}}$, and $\lambda_{\text{HR}}$ associated with input, reconstructed, and DNS reference fields are marked along with the corresponding instantaneous fields. (f) Enlarged views of the boxed regions in (b)-(e) highlight differences in generated vortex structures relative to the high‑resolution reference. (g) Wavenumber spectra for all velocity components ($u, v, w$) comparing SoZoGAN generations (aligned case), coarse inputs, and DNS references. $E_{uu}$ is scaled by $1\times10^4$, $E_{vv}$ by $1\times10^2$, and $E_{ww}$ remains unscaled for clarity. The dash line represents the cut-off wavenumber of the LR input.
• Figure 4: Zonal decomposition and Taylor microscale estimation in TBL super-resolution using SoZoGAN. (a) Hierarchical clustering partitioning the low-resolution TBL domain into three physically meaningful subdomains, with interfaces at $y^+ \approx 102$ and $y^+ \approx 410$, corresponding to the viscous plus lower log-low, upper log-law, and wake regions, respectively. (b) Wall-normal profiles of the estimated Taylor microscale ($\lambda$) predicted by the MLP based on macroscale parameters from low-resolution input, compared with the high-resolution DNS reference.
• Figure 5: Effects of microscale alignment and zonal generation and on TBL super-resolution. (a)-(e) Instantaneous fields of three velocity components (b)-(d) globally generated by SRGANs and (e) zonally generated by SoZoGAN, with $R^2$ values shown below each field. (f) Local zoom‑in views of the black dashed boxes shown in (a), (d) and (e), highlighting the generated near‑wall small‑scale structures of the SRGAN ($\lambda_{\rm train}\approx\ \lambda_{\rm TBL}$) and SoZoGAN, compared with the DNS reference field.