Information Recovery Across Scales in Two-Dimensional Turbulence Using Fourier Neural Operators

Information transfer across scales is a fundamental feature of many complex systems, including turbulent fluid flows. In two-dimensional turbulence, energy propagates through both forward and inverse cascades. Here, we investigate how structured information introduced into a turbulent flow evolves across frequency scales. Using Jax-CFD, we simulate two-dimensional Navier-Stokes dynamics forced with custom forcing patterns based on MNIST digits. The resulting vorticity fields are filtered into high and low frequency components, which are then used to train a Fourier Neural Operator (FNO) to recover the forcing functions. The FNO is able to recover the forcing functions across a range of Reynolds numbers, suggesting that information transferred between scales is recoverable in chaotic fluid systems.