Machine learning methods for the prediction of micromagnetic magnetization dynamics

Abstract

Machine learning (ML) entered the field of computational micromagnetics only recently. The main objective of these new approaches is the automatization of solutions of parameter-dependent problems in micromagnetism such as fast response curve estimation modeled by the Landau-Lifschitz-Gilbert (LLG) equation. Data-driven models for the solution of time- and parameter-dependent partial differential equations require high dimensional training data-structures. ML in this case is by no means a straight-forward trivial task, it needs algorithmic and mathematical innovation. Our work introduces theoretical and computational conceptions of certain kernel and neural network based dimensionality reduction approaches for efficient prediction of solutions via the notion of low-dimensional feature space integration. We introduce efficient treatment of kernel ridge regression and kernel principal component analysis via low-rank approximation. A second line follows neural network (NN) autoencoders as nonlinear data-dependent dimensional reduction for the training data with focus on accurate latent space variable description suitable for a feature space integration scheme. We verify and compare numerically by means of a NIST standard problem. The low-rank kernel method approach is fast and surprisingly accurate, while the NN scheme can even exceed this level of accuracy at the expense of significantly higher costs.

References in corpus (8)

• Adam: A Method for Stochastic Optimization
• Deep Fluids: A Generative Network for Parameterized Fluid Simulations
• Micromagnetics of rare-earth efficient permanent magnets
• Numerical Methods for the Stray-Field Calculation: A Comparison of recently developed Algorithms
• Learning magnetization dynamics
• Learning time-stepping by nonlinear dimensionality reduction to predict magnetization dynamics
• Prediction of magnetization dynamics in a reduced dimensional feature space setting utilizing a low-rank kernel method
• A magnetostatic energy formula arising from the $L^2$-orthogonal decomposition of the stray field

Cited by in corpus (4)

• Forecasting the outcome of spintronic experiments with Neural Ordinary Differential Equations
• Physics-informed machine learning and stray field computation with application to micromagnetic energy minimization
• Magnetoelastic Interactions Reduce Hysteresis in Soft Magnets
• Higher order stray field computation on tensor product domains