  We demonstrate the use of model order reduction and neural networks for
estimating the hysteresis properties of nanocrystalline permanent magnets from
microstructure. With a data-driven approach, we learn the demagnetization curve
from data-sets created by grain growth and micromagnetic simulations. We show
that the granular structure of a magnet can be encoded within a low-dimensional
latent space. Latent codes are constructed using a variational autoencoder. The
mapping of structure code to hysteresis properties is a multi-target regression
problem. We apply deep neural network and use parameter sharing, in order to
predict anchor points along the demagnetization curves from the magnet's
structure code. The method is applied to study the magnetic properties of
nanocrystalline permanent magnets. We show how new grain structures can be
generated by interpolation between two points in the latent space and how the
magnetic properties of the resulting magnets can be predicted.
