Friday, 10:30 - 10:55 h, Room: MA 415


Andreas Schmidt
POD reduced-order modeling in the context of direct-approach optimization

Coauthors: Hans-Georg Bock, Stefan K├Ârkel


To solve optimization problems that involve PDE constraints in general two approaches are distinguished, namely the direct and the indirect approach where we either `first discretize - then optimize' or `first optimize - then discretize'. If Proper Orthogonal Decomposition (POD) is used to reduce the size of the optimization problem in most of
the applications this takes place in the indirect setting.
We will consider the use of POD in a direct-approach setting together with time-dependent PDEs. We can see that a naive application of POD will result in a reduced-order model that lacks the essential property to reflect derivative information of the original high-fidelity model. A remedy to overcome this is the inclusion of necessary derivative information obtained from the high-fidelity model. We will see that
the resulting `enriched' reduced-order model has very beneficial properties. More specifically we obtain accurate approximations to the original problem of either forward derivatives or adjoint derivatives. Furthermore the derivatives will always be consistent even for changing
parameter configurations.


Talk 1 of the contributed session Fri.1.MA 415
"Reduced order model based optimization" [...]
Cluster 19
"PDE-constrained optimization & multi-level/multi-grid methods" [...]


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