Stochastic Optimal Control of Finite Ensembles of Nanomagnets

We control ferromagnetic N -spin dynamics in the presence of thermal fluctuations by minimizing a quadratic functional subject to the stochastic Landau–Lifshitz–Gilbert equation. Existence of a weak solution of the stochastic optimal control problem is shown. The related first order optimality condi...

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Bibliographic Details
Published inJournal of scientific computing Vol. 74; no. 2; pp. 872 - 894
Main Authors Dunst, Thomas, Prohl, Andreas
Format Journal Article
LanguageEnglish
Published New York Springer US 01.02.2018
Springer Nature B.V
Subjects
Algorithms
Anisotropy
Computational Mathematics and Numerical Analysis
Ferromagnetism
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Monte Carlo simulation
Optimal control
Optimization
Random variables
Spin dynamics
Theoretical
Ferromagnetism
Stochastic gradient method
Simulation
Stochastic optimal control
Forward–backward stochastic differential equation
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Summary:We control ferromagnetic N -spin dynamics in the presence of thermal fluctuations by minimizing a quadratic functional subject to the stochastic Landau–Lifshitz–Gilbert equation. Existence of a weak solution of the stochastic optimal control problem is shown. The related first order optimality conditions consist of a coupled forward–backward SDE system, which is numerically solved by a structure-inheriting discretization, the least squares Monte-Carlo method to approximate related conditional expectations, and the new stochastic gradient method. Computational experiments are reported which motivate optimal controls in the case of interacting anisotropy, stray field, exchange energies, and acting noise.
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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-017-0474-z