Application of machine learning to two-dimensional Dzyaloshinskii-Moriya ferromagnets

Principles of machine learning are applied to spin configurations generated by Monte Carlo method on Dzyaloshinskii-Moriya ferromagnetic models hosting the skyrmion phase in two dimensions. Successful feature predictions regarding the average spin chirality, magnetization, as well as magnetic field and temperature, were possible with the machine-learning architecture consisting of convolutional and dense neural network layers. Algorithms trained solely on the xy or z component of the local magnetization were as effective as the one trained on the full xyz component of the input spin configuration in predicting various features. The predictive capacity of the algorithm extended beyond those configurations generated by the model used to make the training configurations, but also those generated by models plagued with disorder. A "scaling procedure" for working with data generated at various length scales is developed and proven to work in a manner analogous to the real-space renormalization process.