  We develop a variational approach to simulating the dynamics of open quantum
many-body systems using deep autoregressive neural networks. The parameters of
a compressed representation of a mixed quantum state are adapted dynamically
according to the Lindblad master equation by employing a time-dependent
variational principle. We illustrate our approach by solving the dissipative
quantum Heisenberg model in one and two dimensions for up to 40 spins and by
applying it to the simulation of confinement dynamics in the presence of
dissipation.
