Satellite microwave radiance observations are strongly sensitive to sea ice, but physical descriptions of the radiative transfer of sea ice and snow are incomplete. Further, the radiative transfer is controlled by poorly-known microstructural properties that vary strongly in time and space. A consequence is that surface-sensitive microwave observations are not assimilated over sea ice areas, and sea ice retrievals use heuristic rather than physical methods. An empirical model for sea ice radiative transfer would be helpful but it cannot be trained using standard machine learning techniques because the inputs are mostly unknown. The solution is to simultaneously train the empirical model and a set of empirical inputs: an “empirical state” method, which draws on both generative machine learning and physical data assimilation methodology. A hybrid physical-empirical network describes the known and unknown physics of sea ice and atmospheric radiative transfer. The network is then trained to fit a year of radiance observations from Advanced Microwave Scanning Radiometer 2 (AMSR2), using the atmospheric profiles, skin temperature and ocean water emissivity taken from a weather forecasting system. This process estimates maps of the daily sea ice concentration while also learning an empirical model for the sea ice emissivity. The model learns to define its own empirical input space along with daily maps of these empirical inputs. These maps represent the otherwise unknown microstructural properties of the sea ice and snow that affect the radiative transfer. This “empirical state” approach could be used to solve many other problems of earth system data assimilation.