Optimizing machine learning models for granular NdFeB magnets by very fast simulated annealing

The macroscopic properties of permanent magnets and the resultant performance required for real implementations are determined by the magnets’ microscopic features. However, earlier micromagnetic simulations and experimental studies required relatively a lot of work to gain any complete and comprehensive understanding of the relationships between magnets’ macroscopic properties and their microstructures. Here, by means of supervised learning, we predict reliable values of coercivity (μ(0)H(c)) and maximum magnetic energy product (BH(max)) of granular NdFeB magnets according to their microstructural attributes (e.g. inter-grain decoupling, average grain size, and misalignment of easy axes) based on numerical datasets obtained from micromagnetic simulations. We conducted several tests of a variety of supervised machine learning (ML) models including kernel ridge regression (KRR), support vector regression (SVR), and artificial neural network (ANN) regression. The hyper-parameters of these models were optimized by a very fast simulated annealing (VFSA) algorithm with an adaptive cooling schedule. In our datasets of randomly generated 1,000 polycrystalline NdFeB cuboids with different microstructural attributes, all of the models yielded similar results in predicting both μ(0)H(c) and BH(max). Furthermore, some outliers, which deteriorated the normality of residuals in the prediction of BH(max), were detected and further analyzed. Based on all of our results, we can conclude that our ML approach combined with micromagnetic simulations provides a robust framework for optimal design of microstructures for high-performance NdFeB magnets.