Magnetostatics and micromagnetics with physics informed neural networks

Author(s)
Alexander Kovacs, Lukas Exl, Alexander Kornell, Johann Fischbacher, Markus Hovorka, Markus Gusenbauer, Leoni Breth, Harald Oezelt, Dirk Praetorius, Dieter Suess, Thomas Schrefl
Abstract

Partial differential equations and variational problems can be solved with physics informed neural networks (PINNs). The unknown field is approximated with neural networks. Minimizing the residuals of the static Maxwell equation at collocation points or the magnetostatic energy, the weights of the neural network are adjusted so that the neural network solution approximates the magnetic vector potential. This way, the magnetic flux density for a given magnetization distribution can be estimated. With the magnetization as an additional unknown, inverse magnetostatic problems can be solved. Augmenting the magnetostatic energy with additional energy terms, micromagnetic problems can be solved. We demonstrate the use of physics informed neural networks for solving magnetostatic problems, computing the magnetization for inverse problems, and calculating the demagnetization curves for two-dimensional geometries.

Organisation(s)
Department of Mathematics, Research Platform MMM Mathematics-Magnetism-Materials, Physics of Functional Materials
External organisation(s)
Donau-Universität Krems, Wolfgang Pauli Institute (WPI) Vienna, Technische Universität Wien, Christian-Doppler-Forschungsgesellschaft
Journal
Journal of Magnetism and Magnetic Materials
Volume
548
No. of pages
12
ISSN
0304-8853
DOI
https://doi.org/10.1016/j.jmmm.2021.168951
Publication date
01-2022
Peer reviewed
Yes
Austrian Fields of Science 2012
103015 Condensed matter
Keywords
ASJC Scopus subject areas
Electronic, Optical and Magnetic Materials, Condensed Matter Physics
Portal url
https://ucris.univie.ac.at/portal/en/publications/magnetostatics-and-micromagnetics-with-physics-informed-neural-networks(921710a2-9604-4381-a59f-28fc9ae13f48).html