Why Your Computer Should Learn the Maxwell-Ampère Equation on its own

Neural networks are powerful tools for modelling unknown or complex functional relations in a relatively simple way. Using cascades of simple operations they can fit highly non-linear functions. In this contribution, we show how neural networks can be used to predict the magnetic field of coils given only the coil geometry. Namely, black-and-white raster graphics are used to present the geometry to the neural net, while colored graphics provide the training data for the respective magnetic field. Using a combination of an auto-encoder layout and elements of convolutional neural nets our network can learn the relationship between simple coil geometries and their generated magnetic fields. Finally, we present the application of such neural networks as surrogate models for the use in optimization problems. Using a surrogate model of the Maxwell-Ampère equation, we are able to find novel induction coil geometries very efficently using an iterative optimization approach rather than performing accurate but very time-consuming conventional simulations.