Input-Output turbulent flow models using Fourier Neural Operators

Identifying linear mappings between flow states can allow for the study of the relative importance of sub-processes and driving mechanisms via input-output analyses. Here we exploit Fourier Neural Operators (FNOs) to learn such linear mappings in turbulent flows, avoiding constraints present in traditional neural networks, in which data pre-processing and a priori knowledge of the needed network architecture are typically required. Our model consists of an FNO with a single linear Fourier layer that, when using the appropriate loss function, is constructed to provide a mapping that can either advance a state variable in time, or map one state variable to another. This FNO architecture is applied to turbulent channel flow and jet-in-crossflow direct numerical simulation data as a precursor to investigating more complicated flows involving turbulence-chemistry interactions.