The modeling of realistic magnetic materials requires the inclusion of defects. Based on the pseudospectral Landau-Lifshitz description of magnetisation dynamics, we propose a statistical model that takes into account defects, specifically vacancies. This statistical model can be integrated with deep learning techniques that correlate defect thresholds with relevant physical observables. We develop a convolutional neural network and a physics-informed neural network combined with theory of functional connections to predict the dispersion relation given defect parameters and physical constraints. A two-branch convolutional neural network is developed to predict domain-wall widths depending on defects threshold, taking into account the spatial profile and domain-wall width separately to achieve a prediction. The proposed physics-informed approaches leverage deep-learning and achieve statistical predictions measured in physical units. This is a stepping stone towards the discovery of new materials and the determination of minimal defect thresholds required for desired dynamics, states, or topological textures.