Magnetic field prediction using generative adversarial networks

Many 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 the reconstruction loss as well as physical losses, our trained generator has learned to predict the missing field values with a mean reconstruction test error of 6.45% when a large single coherent region of field points is missing, and 10.04%, when only a few point measurements in space are available. This is better by about a factor of two compared to conventional methods such as linear interpolation, splines, and biharmonic equations. We verify the results on an experimentally validated magnetic field.