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Stochastic Optimal Control of Finite Ensembles of Nanomagnets

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Abstract

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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Authors and Affiliations

  1. Mathematisches Institut der Universität Tübingen, Auf der Morgenstelle 10, 72076, Tübingen, Germany

    Thomas Dunst & Andreas Prohl

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  1. Thomas Dunst
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  2. Andreas Prohl
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Correspondence to Andreas Prohl.

Additional information

The authors are grateful to helpful discussions with U. Nowak (Universität Konstanz). This work was performed on the computational resource bwUniCluster funded by the Ministry of Science, Research and the Arts Baden-Württemberg and the Universities of the State of Baden-Württemberg, Germany, within the framework program bwHPC.

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Dunst, T., Prohl, A. Stochastic Optimal Control of Finite Ensembles of Nanomagnets. J Sci Comput 74, 872–894 (2018). https://doi.org/10.1007/s10915-017-0474-z

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  • DOI: https://doi.org/10.1007/s10915-017-0474-z

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