Learning optimal multigrid smoothers via neural networks

Understand

Multigrid methods are one of the most efficient techniques for solving linear systems arising from Partial Differential Equations (PDEs) and graph Laplacians from machine learning applications.

• One of the key components of multigrid is smoothing, which aims at reducing high-frequency errors on each grid level.
• However, finding optimal smoothing algorithms is problem-dependent and can impose challenges for many problems.
• In this paper, we propose an efficient adaptive framework for learning optimized smoothers from operator stencils in the form of convolutional neural networks (CNNs).