Lossy Compression in Optimal Control of Cardiac Defibrillation

Please always quote using this URN: urn:nbn:de:0297-zib-18566
  • 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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Author:Sebastian Götschel, Chamakuri Nagaiah, Karl Kunisch, Martin WeiserORCiD
Document Type:ZIB-Report
Tag:Newton-CG; compression; defibrillation; monodomain model; optimal control; trajectory storage
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K57 Reaction-diffusion equations
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Qxx Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] / 35Q92 PDEs in connection with biology and other natural sciences
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Mxx Numerical methods [See also 90Cxx, 65Kxx] / 49M15 Newton-type methods
65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area) / 68Pxx Theory of data / 68P30 Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) [See also 94Axx]
94-XX INFORMATION AND COMMUNICATION, CIRCUITS / 94Axx Communication, information / 94A29 Source coding [See also 68P30]
Date of first Publication:2013/05/24
Series (Serial Number):ZIB-Report (13-26)
ISSN:1438-0064
Published in:published in J. Sci. Comput., 60(1):35-59 (2014)