  We consider $d$-dimensional open quantum lattices whose time evolution is
governed by a master equation which is weakly symmetric under the action of a
finite group $G$ that is a subgroup of all the possible permutations of the
lattice sites. We show that, whenever the steady state is unique, one can
introduce a neural network representation for the system density operator that
explicitly accounts for the system symmetries and can be efficiently optimized
by exploring only a relevant subspace of the parameter space. In particular, as
a proof of principle, we demonstrate the validity of our approach by
determining the steady state structure of the one dimensional dissipative XYZ
model in the presence of a uniform magnetic field.
