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Lossy Compression in Optimal Control of Cardiac Defibrillation

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Abstract

This paper presents efficient computational techniques for solving an optimization problem in cardiac defibrillation governed by the monodomain equations. Time-dependent electrical currents injected at different spatial positions act as the control. Inexact Newton-CG methods are used, with reduced gradient computation by adjoint solves. In order to reduce the computational complexity, adaptive mesh refinement for state and adjoint equations is performed. To reduce the high storage and bandwidth demand imposed by adjoint gradient and Hessian-vector evaluations, a lossy compression technique for storing trajectory data is applied. An adaptive choice of quantization tolerance based on error estimates is developed in order to ensure convergence. The efficiency of the proposed approach is demonstrated on numerical examples.

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Acknowledgments

The authors gratefully acknowledge support by the Austrian Science Foundation (FWF) under SFB 032, “Mathematical Optimization and Applications in Biomedical Sciences”, the Austrian Academy of Sciences (ÖAW) and by the DFG Research Center Matheon, project F9.

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Authors and Affiliations

  1. Zuse Institute Berlin, Takustr. 7, 14195 , Berlin, Germany

    S. Götschel & M. Weiser

  2. Radon Institute for Computational and Applied Mathematics, Altenbergerstr. 69, 4040 , Linz, Austria

    N. Chamakuri & K. Kunisch

  3. Institute of Mathematics and Scientific Computing, University of Graz, Heinrichstr. 36, 8010 , Graz, Austria

    K. Kunisch

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  1. S. Götschel
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  2. N. Chamakuri
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  3. K. Kunisch
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  4. M. Weiser
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Correspondence to S. Götschel.

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Götschel, S., Chamakuri, N., Kunisch, K. et al. Lossy Compression in Optimal Control of Cardiac Defibrillation. J Sci Comput 60, 35–59 (2014). https://doi.org/10.1007/s10915-013-9785-x

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