  Quantum systems interacting with an unknown environment are notoriously
difficult to model, especially in presence of non-Markovian and
non-perturbative effects. Here we introduce a neural network based approach,
which has the mathematical simplicity of the
Gorini-Kossakowski-Sudarshan-Lindblad master equation, but is able to model
non-Markovian effects in different regimes. This is achieved by using recurrent
neural networks for defining Lindblad operators that can keep track of memory
effects. Building upon this framework, we also introduce a neural network
architecture that is able to reproduce the entire quantum evolution, given an
initial state. As an application we study how to train these models for quantum
process tomography, showing that recurrent neural networks are accurate over
different times and regimes.
