  We investigate the problem of determining the Hamiltonian of a locally
interacting open-quantum system. To do so, we construct model estimators based
on inverting a set of stationary, or dynamical, Heisenberg-Langevin equations
of motion which rely on a polynomial number of measurements and parameters. We
validate our Hamiltonian assignment methods by numerically simulating
one-dimensional XX-interacting spin chains coupled to thermal reservoirs. We
study Hamiltonian learning in the presence of systematic noise and find that,
in certain time dependent cases, the Hamiltonian estimator accuracy increases
when relaxing the environment's physicality constraints.
