Thomas Schrefl

Lukas Exl, Winfried Auzinger, Simon Bance et al.

A direct integration algorithm is described to compute the magnetostatic field and energy for given magnetization distributions on not necessarily uniform tensor grids. We use an analytically-based tensor approximation approach for function-related tensors, which reduces calculations to multilinear algebra operations. The algorithm scales with N^(4/3) for N computational cells used and with N^(2/3) (sublinear) when magnetization is given in canonical tensor format. In the final section we confirm our theoretical results concerning computing times and accuracy by means of numerical examples.

Lukas Exl, Claas Abert, Norbert J. Mauser et al.

We derive a Kronecker product approximation for the micromagnetic long range interactions in a collocation framework by means of separable sinc quadrature. Evaluation of this operator for structured tensors (Canonical format, Tucker format, Tensor Trains) scales below linear in the volume size. Based on efficient usage of FFT for structured tensors, we are able to accelerate computations to quasi linear complexity in the number of collocation points used in one dimension. Quadratic convergence of the underlying collocation scheme as well as exponential convergence in the separation rank of the approximations is proved. Numerical experiments on accuracy and complexity confirm the theoretical results.

Alexander Kovacs, Lukas Exl, Alexander Kornell et al.

We introduce conditional PINNs (physics informed neural networks) for estimating the solution of classes of eigenvalue problems. The concept of PINNs is expanded to learn not only the solution of one particular differential equation but the solutions to a class of problems. We demonstrate this idea by estimating the coercive field of permanent magnets which depends on the width and strength of local defects. When the neural network incorporates the physics of magnetization reversal, training can be achieved in an unsupervised way. There is no need to generate labeled training data. The presented test cases have been rigorously studied in the past. Thus, a detailed and easy comparison with analytical solutions is made. We show that a single deep neural network can learn the solution of partial differential equations for an entire class of problems.

Markus Gusenbauer, Harald Oezelt, Johann Fischbacher et al.

Microstructural features play an important role for the quality of permanent magnets. The coercivity is greatly influenced by crystallographic defects, which is well known for MnAl-C, for example. In this work we show a direct link of microstructural features to the local coercivity of MnAl-C grains by machine learning. A large number of micromagnetic simulations is performed directly from Electron Backscatter Diffraction (EBSD) data using an automated meshing, modeling and simulation procedure. Decision trees are trained with the simulation results and predict local switching fields from new microscopic data within seconds.