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.
Metadaten
Author:Martin WeiserORCiD, Sebastian Götschel
Document Type:Article
Parent Title (English):SIAM J. Sci. Comput.
Volume:34
Issue:1
First Page:A161
Last Page:A184
Year of first publication:2012
Preprint:urn:nbn:de:0297-zib-11676
DOI:https://doi.org/10.1137/11082172X