Magnetostatics and micromagnetics with physics informed neural networks

TL;DR

This paper demonstrates how physics informed neural networks can be applied to solve magnetostatic and micromagnetic problems, including inverse problems and demagnetization curves, by approximating magnetic fields and energies.

Contribution

It introduces a neural network-based approach to solve magnetostatic and micromagnetic PDEs and inverse problems using physics informed neural networks.

Findings

Successfully solves magnetostatic problems with PINNs

Computes magnetization in inverse problems

Calculates demagnetization curves for 2D geometries

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.