A surrogate model for data-driven magnetic stray field calculations

TL;DR

This paper introduces a data-driven surrogate model for predicting magnetic stray fields in micro-heterogeneous materials, utilizing stochastic modeling and neural network architectures to replace time-consuming FEM simulations.

Contribution

The paper presents a novel combination of stochastic transition matrices and neural network architectures, specifically UResNet and Fourier CNNs, for efficient microstructure encoding and surrogate modeling.

Findings

The surrogate model accurately predicts magnetic stray fields for unseen microstructures.

The Fourier CNN based on discrete Fourier transform performs comparably to the DCT-based model.

The surrogate model significantly reduces computational time compared to FE$^2$ simulations.

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 sets, FEM simulations appear to be too time consuming. Hence, a stochastic model based on Brownian motion, which utilizes an efficient evaluation of stochastic transition matrices, is applied for the training data generation. For the encoding of the microstructure and the optimization of the surrogate model, two architectures are compared, i.e. the so-called UResNet model and the Fourier Convolutional neural network (FCNN). Here we analyze two FCNNs, one based on the discrete cosine transformation and one based on the complex-valued discrete Fourier transformation. Finally, we compare the magnetic stray fields for independent microstructures (not used in the training set) with results from the FE$^2$ method, a numerical homogenization scheme, to demonstrate the efficiency of the proposed surrogate model.