  We present a novel deep learning-based algorithm to accelerate - through the
use of Artificial Neural Networks (ANNs) - the convergence of Algebraic
Multigrid (AMG) methods for the iterative solution of the linear systems of
equations stemming from finite element discretizations of Partial Differential
Equations (PDE). We show that ANNs can be successfully used to predict the
strong connection parameter that enters in the construction of the sequence of
increasingly smaller matrix problems standing at the basis of the AMG
algorithm, so as to maximize the corresponding convergence factor of the AMG
scheme. To demonstrate the practical capabilities of the proposed algorithm,
which we call AMG-ANN, we consider the iterative solution of the algebraic
system of equations stemming from finite element discretizations of
two-dimensional model problems. First, we consider an elliptic equation with a
highly heterogeneous diffusion coefficient and then a stationary Stokes
problem. We train (off-line) our ANN with a rich dataset and present an
in-depth analysis of the effects of tuning the strong threshold parameter on
the convergence factor of the resulting AMG iterative scheme.
