Scalable physical source-to-field inference with hypernetworks

We present a generative model that amortises computation for the field around e.g. gravitational or magnetic sources. Exact numerical calculation has either computational complexity $\mathcal{O}(M\times{}N)$ in the number of sources and field evaluation points, or requires a fixed evaluation grid to exploit fast Fourier transforms. Using an architecture where a hypernetwork produces an implicit representation of the field around a source collection, our model instead performs as $\mathcal{O}(M + N)$, achieves accuracy of $\sim\!4\%-6\%$, and allows evaluation at arbitrary locations for arbitrary numbers of sources, greatly increasing the speed of e.g. physics simulations. We also examine a model relating to the physical properties of the output field and develop two-dimensional examples to demonstrate its application. The code for these models and experiments is available at https://github.com/cmt-dtu-energy/hypermagnetics.

Magnetic Field Prediction Using Generative Adversarial Networks

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.