  The geometric multigrid algorithm is an efficient numerical method for
solving a variety of elliptic partial differential equations (PDEs). The method
damps errors at progressively finer grid scales, resulting in faster
convergence compared to iterative methods such as Gauss-Seidel. The
prolongation or coarse-to-fine interpolation operator within the multigrid
algorithm, lends itself to a data-driven treatment with deep learning
super-resolution, commonly used to increase the resolution of images. We (i)
propose the integration of a super-resolution generative adversarial network
(GAN) model with the multigrid algorithm as the prolongation operator and (ii)
show that the GAN-interpolation can improve the convergence properties of
multigrid in comparison to cubic spline interpolation on a class of multiscale
PDEs typically solved in fluid mechanics and engineering simulations. We also
highlight the importance of characterizing hybrid (machine
learning/traditional) algorithm parameters.
