Within this project we will devise hybrid simulation methods, that combine numerical time evolution of NQS with quantum simulation of the same physical situation. We foresee synergetic advantages of the hybrid approach, as incorporating data from the quantum simulation may render the numerical simulation more efficient and, reversely, the obtained classical state representations may allow the investigation of properties inaccessible in the experiment. This new method will be the basis for us to investigate dynamics in two-dimensional Bose-Hubbard models realized in the experimental labs of the research unit. We will moreover extend the approach to develop a novel scheme for (approximate) many-body state tomography based on time evolution native to the quantum simulation platform.