  We propose new strategies to handle polygonal grids refinement based on
Convolutional Neural Networks (CNNs). We show that CNNs can be successfully
employed to identify correctly the "shape" of a polygonal element so as to
design suitable refinement criteria to be possibly employed within adaptive
refinement strategies. We propose two refinement strategies that exploit the
use of CNNs to classify elements' shape, at a low computational cost. We test
the proposed idea considering two families of finite element methods that
support arbitrarily shaped polygonal elements, namely Polygonal Discontinuous
Galerkin (PolyDG) methods and Virtual Element Methods (VEMs). We demonstrate
that the proposed algorithms can greatly improve the performance of the
discretization schemes both in terms of accuracy and quality of the underlying
grids. Moreover, since the training phase is performed off-line and is problem
independent the overall computational costs are kept low.
