An effective method for parameter estimation with PDE constraints with multiple right hand sides

TitleAn effective method for parameter estimation with {PDE} constraints with multiple right hand sides
Publication TypeJournal Article
Year of Publication2012
AuthorsEldad Haber, Matthias Chung, Felix J. Herrmann
JournalSIAM Journal on Optimization
PublisherUBC-Earth and Ocean Sciences Department
KeywordsFWI, Optimization, SLIM

Often, parameter estimation problems of parameter-dependent PDEs involve multiple right-hand sides. The computational cost and memory requirements of such problems increase linearly with the number of right-hand sides. For many applications this is the main bottleneck of the computation. In this paper we show that problems with multiple right-hand sides can be reformulated as stochastic programming problems by combining the right-hand sides into a few „simultaneous” sources. This effectively reduces the cost of the forward problem and results in problems that are much cheaper to solve. We discuss two solution methodologies: namely sample average approximation and stochastic approximation. To illustrate the effectiveness of our approach we present two model problems, direct current resistivity and seismic tomography.

Citation Keyhaber10TRemp