Spectrally Decomposed Diffusion Models for Generative Turbulence Recovery

TL;DR

This paper introduces a spectral filtering-based super-resolution approach using generative machine learning to recover missing turbulent features in fluid flows, effectively doubling the high-wavenumber range in Kolmogorov turbulence.

Contribution

It develops a novel two-stage spectral filtering method for super-resolution in turbulence data, extending prior techniques to recover high-wavenumber turbulence components.

Findings

Successfully upsampled turbulence data by 8x

Doubled the range of recoverable wavenumbers

Validated statistical turbulence properties of generated samples

Abstract

We investigate the statistical recovery of missing physics and turbulent phenomena in fluid flows using generative machine learning. Here we develop a two-stage super-resolution method using spectral filtering to restore the high-wavenumber components of a Kolmogorov flow. We include a rigorous examination of generated samples through the lens of statistical turbulence. By extending the prior methods to a combined super-resolution and conditional high-wavenumber generation, we demonstrate turbulence recovery on a 8x upsampling task, effectively doubling the range of recovered wavenumbers.