Magnetostatics and micromagnetics with physics informed neural networks

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.

22 pages, 9 figures

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• Magnetic Field Prediction Using Generative Adversarial Networks
• Physics-informed machine learning and stray field computation with application to micromagnetic energy minimization
• Combination of Measurement Data and Domain Knowledge for Simulation of Halbach Arrays with Bayesian Inference
• Higher order stray field computation on tensor product domains
• Computational Frameworks for Patterned Two-Dimensional Magnetism
• Modern triad for magnetic material science: geometric shape, electronic bands and spin textures