In this talk, we present a multilevel neural network approach for approximating the solution mapping of the parametric Darcy problem. Our architecture is constructed using a multilevel cascade of CNNs configured similarly to the multigrid F-Cycle. We show that common multilevel CNN architectures are able to approximate multigrid cycles arbitrarily well. More specifically, U-Net architectures alone are able to approximate multigrid solver steps for the parametric Darcy problem without considerable overhead, thus beating the curse of dimensionality. Furthermore, we solidify our theoretical findings by presenting state-of-the-art numerical results on a wide variety of test cases.