State Trajectory Compression for Optimal Control with Parabolic PDEs

Please always quote using this URN: urn:nbn:de:0297-zib-11676
  • In optimal control problems with nonlinear time-dependent 3D PDEs, full 4D discretizations are usually prohibitive due to the storage requirement. For this reason gradient and quasi-Newton methods working on the reduced functional are often employed. The computation of the reduced gradient requires one solve of the state equation forward in time, and one backward solve of the adjoint equation. The state enters into the adjoint equation, again requiring the storage of a full 4D data set. We propose a lossy compression algorithm using an inexact but cheap predictor for the state data, with additional entropy coding of prediction errors. As the data is used inside a discretized, iterative algorithm, lossy coding maintaining an error bound is sufficient.

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Author:Martin WeiserORCiD, Sebastian Götschel
Document Type:ZIB-Report
Tag:adjoint gradient computation; optimal control; trajectory storage
MSC-Classification:49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Mxx Numerical methods [See also 90Cxx, 65Kxx] / 49M29 Methods involving duality
65-XX NUMERICAL ANALYSIS / 65Kxx Mathematical programming, optimization and variational techniques / 65K10 Optimization and variational techniques [See also 49Mxx, 93B40]
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
94-XX INFORMATION AND COMMUNICATION, CIRCUITS / 94Axx Communication, information / 94A29 Source coding [See also 68P30]
Date of first Publication:2010/03/22
Series (Serial Number):ZIB-Report (10-05)
Published in:Appeared in: SIAM J. Sci. Comp. 34 (1): A161-A184, 2012