  Plenty of scientific and real-world applications are built on magnetic fields
and their characteristics. To retrieve the valuable magnetic field information
in high resolution, extensive field measurements are required, which are either
time-consuming to conduct or even not feasible due to physical constraints. To
alleviate this problem, we predict magnetic field values at a random point in
space from a few point measurements by using a generative adversarial network
(GAN) structure. The deep learning (DL) architecture consists of two neural
networks: a generator, which predicts missing field values of a given magnetic
field, and a critic, which is trained to calculate the statistical distance
between real and generated magnetic field distributions. By minimizing this
statistical distance, a reconstruction loss as well as physical losses, our
trained generator has learned to predict the missing field values with a median
reconstruction test error of 5.14%, when a single coherent region of field
points is missing, and 5.86%, when only a few point measurements in space are
available and the field measurements around are predicted. We verify the
results on an experimentally validated field.
