  Algebraic multigrid (AMG) methods are among the most efficient solvers for
linear systems of equations and they are widely used for the solution of
problems stemming from the discretization of Partial Differential Equations
(PDEs). The most severe limitation of AMG methods is the dependence on
parameters that require to be fine-tuned. In particular, the strong threshold
parameter is the most relevant since it stands at the basis of the construction
of successively coarser grids needed by the AMG methods. We introduce a novel
Deep Learning algorithm that minimizes the computational cost of the AMG method
when used as a finite element solver. We show that our algorithm requires
minimal changes to any existing code. The proposed Artificial Neural Network
(ANN) tunes the value of the strong threshold parameter by interpreting the
sparse matrix of the linear system as a black-and-white image and exploiting a
pooling operator to transform it into a small multi-channel image. We
experimentally prove that the pooling successfully reduces the computational
cost of processing a large sparse matrix and preserves the features needed for
the regression task at hand. We train the proposed algorithm on a large dataset
containing problems with a highly heterogeneous diffusion coefficient defined
in different three-dimensional geometries and discretized with unstructured
grids and linear elasticity problems with a highly heterogeneous Young's
modulus. When tested on problems with coefficients or geometries not present in
the training dataset, our approach reduces the computational time by up to 30%.
