  Recently, progress has been made in the application of neural networks to the
numerical analysis of partial differential equations (PDEs). In the latter the
variational formulation of the Poisson problem is used in order to obtain an
objective function - a regularised Dirichlet energy - that was used for the
optimisation of some neural networks. In this notes we use the notion of
$\Gamma$-convergence to show that ReLU networks of growing architecture that
are trained with respect to suitably regularised Dirichlet energies converge to
the true solution of the Poisson problem. We discuss how this approach
generalises to arbitrary variational problems under certain universality
assumptions of neural networks and see that this covers some nonlinear
stationary PDEs like the $p$-Laplace.
