Spectrally decomposed denoising diffusion probabilistic models for generative turbulence super-resolution

We investigate the statistical recovery of missing physics and turbulent phenomena in fluid flows using generative machine learning. Here, we develop and test a two-stage super-resolution method using spectral filtering to restore the high-wavenumber components of two flows: Kolmogorov flow and Rayleigh-B & eacute;nard convection. We include a rigorous examination of the generated samples via systematic assessment of the statistical properties of turbulence. The present approach extends prior methods to augment an initial super-resolution with a conditional high-wavenumber generation stage. We demonstrate recovery of fields with statistically accurate turbulence on an 8x upsampling task for both the Kolmogorov flow and the Rayleigh-B & eacute;nard convection, significantly increasing the range of recovered wavenumbers from the initial super-resolution.