Micromagnetics encompasses a theoretical framework aimed at outlining the arrangement of magnetization within ferromagnetic substances across a continuous spectrum. The behavior of ferromagnetic materials is regulated by the Landau–Lifshitz equation, a highly nonlinear equation characterized by a non-convex constraint. This chapter introduces an innovative approach to tackle the Landau–Lifshitz equations in high-dimensional space. Our method integrates nonlinear Feynman–Kac formulations with Deep Learning techniques to achieve enhanced solutions. The Landau–Lifshitz equation can be transformed into Backward Stochastic Differential Equations to establish a robust framework for computational analysis. Our approach, which involves the use of advanced mathematical tools and deep learning models, is highly effective in capturing the intricate dynamics of magnetic moments.

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Deep Learning Approach for Micromagnetism Modeling

  • Fatima-Ezzahrae Bahou,
  • Mohammed Moumni,
  • Yassine Sabbar

摘要

Micromagnetics encompasses a theoretical framework aimed at outlining the arrangement of magnetization within ferromagnetic substances across a continuous spectrum. The behavior of ferromagnetic materials is regulated by the Landau–Lifshitz equation, a highly nonlinear equation characterized by a non-convex constraint. This chapter introduces an innovative approach to tackle the Landau–Lifshitz equations in high-dimensional space. Our method integrates nonlinear Feynman–Kac formulations with Deep Learning techniques to achieve enhanced solutions. The Landau–Lifshitz equation can be transformed into Backward Stochastic Differential Equations to establish a robust framework for computational analysis. Our approach, which involves the use of advanced mathematical tools and deep learning models, is highly effective in capturing the intricate dynamics of magnetic moments.