  We discuss Hamiltonian and Liouvillian learning for analog quantum simulation
from non-equilibrium quench dynamics in the limit of weakly dissipative
many-body systems. We present various strategies to learn the operator content
of the Hamiltonian and the Lindblad operators of the Liouvillian. We compare
different ans\"atze based on an experimentally accessible "learning error"
which we consider as a function of the number of runs of the experiment.
Initially, the learning error decreasing with the inverse square root of the
number of runs, as the error in the reconstructed parameters is dominated by
shot noise. Eventually the learning error remains constant, allowing us to
recognize missing ansatz terms. A central aspect of our approach is to
(re-)parametrize ans\"atze by introducing and varying the dependencies between
parameters. This allows us to identify the relevant parameters of the system,
thereby reducing the complexity of the learning task. Importantly, this
(re-)parametrization relies solely on classical post-processing, which is
compelling given the finite amount of data available from experiments. A
distinguishing feature of our approach is the possibility to learn the
Hamiltonian, without the necessity of learning the complete Liouvillian, thus
further reducing the complexity of the learning task. We illustrate our method
with two, experimentally relevant, spin models.
