  Algebraic or geometric multigrid methods are commonly used in numerical
solvers as they are a multi-resolution method able to handle problems with
multiple scales. In this work, we propose a modification to the commonly-used
U-Net neural network architecture that is inspired by the principles of
multigrid methods, referred to here as U-Net-MG. We then demonstrate that this
proposed U-Net-MG architecture can successfully reduce the test prediction
errors relative to the conventional U-Net architecture when modeling a set of
fluid dynamic problems. In total, we demonstrate an improvement in the
prediction of velocity and pressure fields for the canonical fluid dynamics
cases of flow past a stationary cylinder, flow past 2 cylinders in out-of-phase
motion, and flow past an oscillating airfoil in both the propulsion and energy
harvesting modes. In general, while both the U-Net and U-Net-MG models can
model the systems well with test RMSEs of less than 1%, the use of the U-Net-MG
architecture can further reduce RMSEs by between 20% and 70%.
