  We present several numerical solutions to a generalized Grad-Shafranov
equation (GGSE), which governs axisymmetric plasma equilibria with
incompressible flows of arbitrary direction, using fully connected,
feed-forward, deep neural networks, also known as multi-layer perceptrons. Such
artificial neural network (ANNs) are trained to approximate tokamak-relevant
equilibria upon minimizing the GGSE mean squared residual in the plasma volume
and the poloidal flux function on the plasma boundary. Solutions for the
Solovev and the general linearizing ansatz for the free functions involved in
the GGSE are obtained and benchmarked against known analytic solutions. We also
construct a non-linear equilibrium incorporating characteristics relevant to
the high confinement mode. In our numerical experiments it was observed that
changing the radial distribution of the training points has a surprisingly
small effect on the accuracy of the trained solution. In particular it is shown
that localizing the training points at the plasma edge results in ANN solutions
that describe quite accurately the entire magnetic configuration, thus
demonstrating the interpolation capabilities of the ANNs.
