Deep learning statistical defect models on magnetic material dynamic and static properties

The modelling 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. Starting with a convolutional neural network, we constructed a layered-learning approach combining elements of a physics-informed neural network with the theory of functional connections for a physics-constrained surrogate to predict specific dispersion relations given defect parameters. A two-branch convolutional neural network is implemented to predict domain-wall widths calculated with defects, and thus a defect threshold is obtained by taking into account the spatial profile and domain-wall width separately for the 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.