A machine-learning approach to magnetic neutron scattering

One of the benefits of magnetic neutron scattering (NS) is that it can constrain the parameters of a pre-existing model Hamiltonian. Here we propose an unbiased approach that can be used before a model has been formulated. It combines Principal Component Analysis (PCA) with an artifical neural network (ANN). The PCA algorithm extracts the essential variables describing a set of NS cross-sections in an unsupervised way. The ANN then uses that information to learn to predict the cross-sections under different conditions, with supervision. To test our method, we apply it to simulated diffuse NS cross-sections obtained by exact diagonalisation of a previously-studied model of molecular magnets [H. R. Irons et al., PRB 96, 224408 (2017)]. Our main result is that the PCA can efficiently "discover" the number of fundamental parameters in the problem. The principal component scores capture key elements of the Physics including entanglement transitions. The ANN can then accurately predict NS cross-sections, confirming the validity of the PCA-based description. We conclude that PCA of NS data from real materials can be a powerful tool, specifically one capable of placing severe constraints on possible model Hamiltonians.