  In this work we apply deep neural networks to find the non-equilibrium steady
state solution to correlated open quantum many-body systems. Motivated by the
ongoing search to find more powerful representations of (mixed) quantum states,
we design a simple prototypical convolutional neural network and show that
parametrizing the density matrix directly with more powerful models can yield
better variational ansatz functions and improve upon results reached by neural
density operator based on the restricted Boltzmann machine. Hereby we give up
the explicit restriction to positive semi-definite density matrices. However,
this is fulfilled again to good approximation by optimizing the parameters. The
great advantage of this approach is that it opens up the possibility of
exploring more complex network architectures that can be tailored to specific
physical properties. We show how translation invariance can be enforced
effortlessly and reach better results with fewer parameters. We present results
for the dissipative one-dimensional transverse-field Ising model and a
two-dimensional dissipative Heisenberg model compared to exact values.
