An efficient Poisson solver and a data-driven surrogate model for magnetic stray field calculations

Abstract In this contribution we propose a data-driven surrogate model for the prediction of magnetic stray fields in two-dimensional random micro-heterogeneous materials. Since data driven models require thousands of training data samples, finite element simulations appear to be too time consuming.To bypass this computational bottleneck, an efficient approach based on Brownian motion and the evaluation of stochastic transition matrices is used to generate a large number of training data in short time. The method presented here is a generalization of an approach that has already been described for the simulation of porous materials with impermeable inclusions. The novel approach is an extension to heterogeneous materials with different magnitudes of permeability. For the encoding of the microstructure and the optimization of the surrogate model, two architectures are compared, i.e., the so-called U-shaped Residual Network (UResNet) model and the Fourier Convolutional Neural Network (FCNN). To demonstrate the workability of the proposed methods numerical examples are employed.