  Artificial Neuronal Networks are models widely used for many scientific
tasks. One of the well-known field of application is the approximation of
high-dimensional problems via Deep Learning. In the present paper we
investigate the Deep Learning techniques applied to Shape Functionals, and we
start from the so--called Torsional Rigidity. Our aim is to feed the Neuronal
Network with digital approximations of the planar domains where the Torsion
problem (a partial differential equation problem) is defined, and look for a
prediction of the value of Torsion. Dealing with images, our choice fell on
Convolutional Neural Network (CNN), and we train such a network using reference
solutions obtained via Finite Element Method. Then, we tested the network
against some well-known properties involving the Torsion as well as an old
standing conjecture. In all cases, good approximation properties and accuracies
occurred.
