Single-snapshot machine learning for super-resolution of turbulence

TL;DR

This paper questions the data-hungry paradigm of turbulence ML by showing that a single flow snapshot can suffice for learning a nonlinear mapping from low- to high-resolution fields. It employs a physics-aware interconnected DSC/MS CNN to perform super-resolution, training on tiles sampled from one snapshot and testing on independent cases, including 2D isotropic turbulence and 3D turbulent channel flow. The main contributions are (a) demonstration of cross-Reynolds-number generalization from a single snapshot, (b) introduction of moment-based, rotation/strain-informed sampling to enhance data efficiency, and (c) evidence that the approach preserves key turbulence statistics (PDFs, energy spectra, correlations) and near-wall features with modest errors. The findings highlight a path toward data-efficient turbulence analyses, with potential practical impact in reducing data requirements for flow reconstruction and analysis while maintaining physical fidelity.

Abstract

Modern machine-learning techniques are generally considered data-hungry. However, this may not be the case for turbulence as each of its snapshots can hold more information than a single data file in general machine-learning settings. This study asks the question of whether nonlinear machine-learning techniques can effectively extract physical insights even from as little as a {\it single} snapshot of turbulent flow. As an example, we consider machine-learning-based super-resolution analysis that reconstructs a high-resolution field from low-resolution data for two examples of two-dimensional isotropic turbulence and three-dimensional turbulent channel flow. First, we reveal that a carefully designed machine-learning model trained with flow tiles sampled from only a single snapshot can reconstruct vortical structures across a range of Reynolds numbers for two-dimensional decaying turbulence. Successful flow reconstruction indicates that nonlinear machine-learning techniques can leverage scale-invariance properties to learn turbulent flows. We also show that training data of turbulent flows can be cleverly collected from a single snapshot by considering characteristics of rotation and shear tensors. Second, we perform the single-snapshot super-resolution analysis for turbulent channel flow, showing that it is possible to extract physical insights from a single flow snapshot even with inhomogeneity. The present findings suggest that embedding prior knowledge in designing a model and collecting data is important for a range of data-driven analyses for turbulent flows. More broadly, this work hopes to stop machine-learning practitioners from being wasteful with turbulent flow data.

Figures (13)

• Figure 1: Interconnected DSC/MS model FFT2023_survey for super-resolution reconstruction of turbulent flows.
• Figure 2: Two-dimensional isotropic vorticity field. Red boxes are example flow tiles used for training.
• Figure 3: The single snapshot super-resolution of two-dimensional decaying turbulence. Its accuracy is assessed with test snapshots from three different simulations. The instantaneous Taylor length scale $\lambda(t)$ for a representative test snapshot is reported along with each $Re_0$. The value underneath each contour is the $L_2$ error norm. The probability density function (PDF) for test snapshots at each Reynolds number is also shown.
• Figure 4: Kinetic energy spectrum $E(k)$ of the reconstructed vorticity fields.
• Figure 5: Example snapshots used for single-snapshot training. The value underneath each snapshot is the instantaneous Taylor length scale $\lambda(t)$.