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Optical imaging through complex media, such as biological tissues or fog, is challenging due to light scattering. In the multiple scattering regime, wavefront shaping provides an effective method to retrieve information; it relies on measuring how the propagation of different optical wavefronts are impacted by scattering. Based on this principle, several wavefront shaping techniques were successfully developed, but most of them are highly invasive and limited to proof-of-principle experiments. Here, we propose to use a neural network approach to non-invasively characterize and control light scattering inside the medium and also to retrieve information of hidden objects buried within it. Unlike most of the recently-proposed approaches, the architecture of our neural network with its layers, connected nodes and activation functions has a true physical meaning as it mimics the propagation of light in our optical system. It is trained with an experimentally-measured input/output dataset built from a series of incident light patterns and corresponding camera snapshots. We apply our physics-based neural network to a fluorescence microscope in epi-configuration and demonstrate its performance through numerical simulations and experiments. This flexible method can include physical priors and we show that it can be applied to other systems as, for example, non-linear or coherent contrast mechanisms.