1167
eng
reportzib
0
2010-03-22
2010-03-22
--
State Trajectory Compression for Optimal Control with Parabolic PDEs
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.
10-05
1438-0064
1228
urn:nbn:de:0297-zib-11676
Appeared in: SIAM J. Sci. Comp. 34 (1): A161-A184, 2012
Martin Weiser
unknown unknown
Sebastian Götschel
ZIB-Report
10-05
eng
uncontrolled
optimal control
eng
uncontrolled
adjoint gradient computation
eng
uncontrolled
trajectory storage
Mathematik
Methods involving duality
Optimization and variational techniques [See also 49Mxx, 93B40]
Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Source coding [See also 68P30]
Numerical Mathematics
Computational Medicine
Götschel, Sebastian
Weiser, Martin
MATHEON-F9
ZIB-Kaskade7
https://opus4.kobv.de/opus4-zib/files/1167/ZR-10-05.pdf