This paper presents a hybrid model to estimate the magnetic behaviour of a ferromagnetic structure. The mathematical-physical model has been developed using the Method of Moments combined with a hysteresis model. The mathematical model was derived by a linearisation of the hysteresis curve. The initial magnetic state of a ferromagnetic object is found through inverse computations, including regularisation techniques. The idea of dictionary regularisation is introduced to support the inverse computations with prescribed templates that reflect a priori knowledge of the typical shapes of magnetisation distributions. These templates are extracted from the Method of Moments. Data assimilation is used to update the model in time by means of measurements of the magnetic field near a ferromagnetic structure. The proposed hybrid model is implemented for a typical steel object and verified by means of numerical experiments and measurements in an experimental environment.