  In many numerical schemes, the computational complexity scales non-linearly
with the problem size. Solving a linear system of equations using direct
methods or most iterative methods is a typical example. Algebraic multi-grid
(AMG) methods are numerical methods used to solve large linear systems of
equations efficiently. One of the main differences between AMG methods is how
the coarser grid is constructed from a given fine grid. There are two main
classes of AMG methods; graph and aggregation based coarsening methods. Here we
propose an aggregation-based coarsening framework leveraging graph
representation learning and clustering algorithms. Our method introduces the
power of machine learning into the AMG research field and opens a new
perspective for future researches. The proposed method uses graph
representation learning techniques to learn latent features of the graph
obtained from the underlying matrix of coefficients. Using these extracted
features, we generated a coarser grid from the fine grid. The proposed method
is highly capable of parallel computations. Our experiments show that the
proposed method's efficiency in solving large systems is closely comparable
with other aggregation-based methods, demonstrating the high capability of
graph representation learning in designing multi-grid solvers.
