  In this contribution we propose a data-driven surrogate model for the
prediction of magnetic stray fields in two-dimensional random
micro-heterogeneous materials. Since data driven models require thousands of
training data sets, FEM simulations appear to be too time consuming. Hence, a
stochastic model based on Brownian motion, which utilizes an efficient
evaluation of stochastic transition matrices, is applied for the training data
generation. For the encoding of the microstructure and the optimization of the
surrogate model, two architectures are compared, i.e. the so-called UResNet
model and the Fourier Convolutional neural network (FCNN). Here we analyze two
FCNNs, one based on the discrete cosine transformation and one based on the
complex-valued discrete Fourier transformation. Finally, we compare the
magnetic stray fields for independent microstructures (not used in the training
set) with results from the FE$^2$ method, a numerical homogenization scheme, to
demonstrate the efficiency of the proposed surrogate model.
