  Computational material modeling using advanced numerical techniques speeds up
the design process and reduces the costs of developing new engineering
products. In the field of multiscale modeling, huge computation efforts are
expected for modeling heterogeneous materials while trying to reach high
accuracy levels. In this work, a machine learning approach, namely the
convolutional neural network (CNN), is developed as a solution providing a high
level of accuracy, while being computationally efficient. The input for the CNN
model consists of two-/three-dimensional images of artificial periodic and
biphasic microstructures in the form of nonoverlapping and overlapping, mono-
and polydisperse circular/spherical disk systems, which are generated by a
random sequential inhibition process. These correspond to Statistical Volume
Elements (SVE). Considering linear magnetostatics at the microscale, the output
is the apparent permeability of the SVE. Training and testing data for the
apparent properties is produced with finite element method-based two-scale
asymptotic homogenization. The model efficiency is revealed by employing some
representative examples in two- and three-dimensional settings. In this regard,
the performance of the CNN model is assessed with the applied computational
homogenization method relating to the accuracy and computational efficiency.
The results with the CNN model show high accuracy in predicting the homogenized
permeability and a significant decrease in computation time.
