Multigrid methods are amongst the most successful strategies for solving linear systems arising from discretized elliptic equations. The main idea is to combine different levels of approximation in a multilevel hierarchy to compute the solution. Common to all these strategies is the need for the transfer of data between different grids. In this talk we give a basic overview of multigrid methods followed by an insight on neural network models, to then investigate the interplay between these two frameworks. We address the crucial points of multigrid using predictions instead of expensive computations, and we discuss how to overcome the ever-increasing complexity of the learning process applying multilevel hierarchies during the training phase.
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