Input-Output Neural Operator model for Jet in Crossflow

A Fourier Neural Operator (FNO)-based network is used as an Input-output model to study Direct Numerical Simulation (DNS) jet-in-crossflow. The network consists of a non-linear encoder and decoder, and a single linear Fourier layer corresponding to the model's latent space, which allows us to obtain a linear mapping between input and output variables in an encoded space. This linear mapping is a powerful tool, enabling us to get an approximation of the Koopman operator, serve as a mapping between spatial regions of the flow, or map one state variable to another. For each case, an appropriate loss function and network setup is implemented. These mappings permit us to draw conclusions regarding the relative importance of sub-processes in a flow through input-output analysis. This network was originally developed and implemented using Large Eddy Simulation (LES) channel flow data, and now performing a coordinate transform of the jet-in-crossflow data into a frame that follows the center streamline of the jet, we analyze this flow in a similar manner.