Machine Learning for Magnetic Phase Diagrams and Inverse Scattering Problems

Abstract: Machine learning promises to deliver powerful new approaches to neutron scattering from magnetic materials. Large scale simulations provide the means to realise this with approaches including spin-wave, Landau Lifshitz, and Monte Carlo methods. These approaches are shown to be effective at simulating magnetic structures and dynamics in a wide range of materials. Using large numbers of simulations the effectiveness of machine learning approaches are assessed. Principal component analysis and nonlinear autoencoders are considered with the latter found to provide a high degree of compression and to be highly suited to neutron scattering problems. Agglomerative heirarchical clustering in the latent space is shown to be effective at extracting phase diagrams of behavior and features in an automated way that aid understanding and interpretation. The autoencoders are also well suited to optimizing model parameters and were found to be highly advantageous over conventional fitting approaches including being tolerant of artifacts in untreated data. The potential of machine learning to automate complex data analysis tasks including the inversion of neutron scattering data into models and the processing of large volumes of multidimensional data is assessed. Directions for future developments are considered and machine learning argued to have high potential for impact on neutron science generally.