Order at the Mesoscale: Connecting supercomputing of compressible convection to classical and quantum machine learning

Turbulent convection flows in nature display prominent patterns in the mesoscale range whose characteristic length in the horizontal directions exceeds the system scale height. Known as the turbulent superstructure of convection, they are absent on both larger and smaller scales and evolve in ways not yet understood; but they are an essential link in the heat and momentum transport to larger scales, an important driver of intermittent fluid motion at sub-mesoscales, and one major source of uncertainty in the prognosis of climate change and space weather. In MesoComp, I will investigate the formation of superstructures in massively parallel simulations of compressible turbulent convection in horizontally extended domains, aiming for a deeper understanding of their dynamical origin and role in the transport of heat and momentum. I will then use these high-fidelity simulations to build recurrent machine learning models to predict the evolution and statistics of the superstructure and thus quantify the transport fluxes beyond the mesoscale. I will also analyse the impact of the mesoscale structures on the highly intermittent statistics at the small-scale of the flow and reveal the resulting feedback in the form of improved subgrid parametrizations by means of generative machine learning. MesoComp opens additional doors to the application of quantum algorithms in machine learning which significantly improve the statistical sampling and data compression properties compared to their classical counterparts. From a longer-term perspective, my research results in a quantum advantage for the numerical analysis of classical turbulence, which accelerates the parametrizations of mesoscale convection and increases their fidelity. This work will finally lead to more precise predictions of the on-going climate change and global warming. The results will also improve solar activity models and thus solar storm prognoses with impacts on satellite communication and electrical grids.