Learning time-stepping by nonlinear dimensionality reduction to predict magnetization dynamics

Abstract

We establish a time-stepping learning algorithm and apply it to predict the solution of the partial differential equation of motion in micromagnetism as a dynamical system depending on the external field as parameter. The data-driven approach is based on nonlinear model order reduction by use of kernel methods for unsupervised learning, yielding a predictor for the magnetization dynamics without any need for field evaluations after a data generation and training phase as precomputation. Magnetization states from simulated micromagnetic dynamics associated with different external fields are used as training data to learn a low-dimensional representation in so-called feature space and a map that predicts the time-evolution in reduced space. Remarkably, only two degrees of freedom in feature space were enough to describe the nonlinear dynamics of a thin-film element. The approach has no restrictions on the spatial discretization and might be useful for fast determination of the response to an external field.

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Cited by in corpus (5)

• Dynamics of reconfigurable artificial spin ice: towards magnonic functional materials
• Magnetostatics and micromagnetics with physics informed neural networks
• Learning magnetization dynamics
• Machine learning methods for the prediction of micromagnetic magnetization dynamics
• Prediction of magnetization dynamics in a reduced dimensional feature space setting utilizing a low-rank kernel method