Physics-informed machine learning and stray field computation with application to micromagnetic energy minimization

Abstract

We study the full 3d static micromagnetic equations via a physics-informed neural network (PINN) ansatz for the continuous magnetization configuration. PINNs are inherently mesh-free and unsupervised learning models. In our approach we can learn to minimize the total Gibbs free energy with additional conditional parameters, such as the exchange length, by a single low-parametric neural network model. In contrast, traditional numerical methods would require the computation and storage of a large number of solutions to interpolate the continuous spectrum of quasi-optimal magnetization configurations. We also consider the important and computationally expensive stray field problem via PINNs, where we use a basically linear learning ansatz, called extreme learning machines (ELM) within a splitting method for the scalar potential. This reduces the stray field training to a linear least squares problem with precomputable solution operator. We validate the stray field method by means of numerical example comparisons from literature and illustrate the full micromagnetic approach via the NIST $\mu$MAG standard problem $\#3$.

arXiv comment17 pages, 10 figures

References in corpus (16)

• On the Variance of the Adaptive Learning Rate and Beyond
• PFNN: A Penalty-Free Neural Network Method for Solving a Class of Second-Order Boundary-Value Problems on Complex Geometries
• LaBonte's method revisited: An effective steepest descent method for micromagnetic energy minimization
• Micromagnetics of rare-earth efficient permanent magnets
• 3D Printing of Polymer Bonded Rare-Earth Magnets With a Variable Magnetic Compound Density for a Predefined Stray Field
• Numerical Methods for the Stray-Field Calculation: A Comparison of recently developed Algorithms
• Magnetostatics and micromagnetics with physics informed neural networks
• Conjugate gradient methods in micromagnetics
• Preconditioned nonlinear conjugate gradient method for micromagnetic energy minimization
• MagTense: a micromagnetic framework using the analytical demagnetization tensor
• Computational Micromagnetics based on Normal Modes: bridging the gap between macrospin and full spatial discretization
• Magnetic Field Prediction Using Generative Adversarial Networks
• Learning magnetization dynamics
• Non-uniform FFT for the finite element computation of the micromagnetic scalar potential
• Machine learning methods for the prediction of micromagnetic magnetization dynamics
• A magnetostatic energy formula arising from the $L^2$-orthogonal decomposition of the stray field

Cited by in corpus (1)

• Higher order stray field computation on tensor product domains