Analysis of downscaled branches and Receptive field on a CNN-based incompressible solver

Convolutional Neural Networks (CNN) are widely used in the CFD community due to their fast predictions and capabilities to extract topological information from fluid flows. While standalone CNNs have been extensively studied, their coupling with a CFD solver still remains unclear, in particular for time-evolving problems. This work focuses on a CNN embedded into an incompressible solver. The neural network solves the Poisson equation, necessary to update the velocity field provided by the resolution of the advection equation. Several U-Net architectures, parametrized by their number of downscaled branches (DBs) and receptive field (RF), are evaluated on the Von Karman oscillations generated by a 2D cylinder at low Reynolds numbers. Results are compared with other standard Poisson and CFD solvers, revealing that the Von Karman oscillations can be reproduced accurately using the CNN-based solver with fast inference time. To further analyze the error, Dynamic Mode Decomposition (DMD) is applied on the solutions, revealing the key effects of both DBs and RF on the modes accuracy, shedding new light on the behavior and limitations of CNN when interacting with CFD solvers.