Spectrally decomposed denoising diffusion probabilistic models for generative turbulence super-resolution
M. Sardar, Alex Skillen, Małgorzata J. Zimoń, Samuel Draycott, Alistair Revell
Abstract
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–Bénard 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 8× upsampling task for both the Kolmogorov flow and the Rayleigh–Bénard convection, significantly increasing the range of recovered wavenumbers from the initial super-resolution.