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

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dc.contributorVirginia Techen
dc.contributor.authorHaber, Eldaden
dc.contributor.authorChung, Matthiasen
dc.contributor.authorHerrmann, Felixen
dc.contributor.departmentMathematicsen
dc.date.accessed2014-05-27en
dc.date.accessioned2014-05-28T18:35:07Zen
dc.date.available2014-05-28T18:35:07Zen
dc.date.issued2012en
dc.description.abstractOften, 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.en
dc.description.sponsorshipNSERC IRC programen
dc.description.sponsorshipTexas State University Research Enhancement Programen
dc.identifier.citationHaber, E.; Chung, M.; Herrmann, F., "An effective method for parameter estimation with pde constraints with multiple right-hand sides," SIAM J. Optim., 22(3), 739-757, (2012). DOI: 10.1137/11081126xen
dc.identifier.doihttps://doi.org/10.1137/11081126xen
dc.identifier.issn1052-6234en
dc.identifier.urihttp://hdl.handle.net/10919/48152en
dc.identifier.urlhttp://epubs.siam.org/doi/abs/10.1137/11081126Xen
dc.language.isoen_USen
dc.publisherSiam Publicationsen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectpde constrained optimizationen
dc.subjectstochastic optimizationen
dc.subjectstochasticen
dc.subjectapproximationen
dc.subjectsample average approximationen
dc.subjectinverse problemsen
dc.subjectparameteren
dc.subjectestimationen
dc.subjectlarge scale problemsen
dc.subjectdc resistivityen
dc.subjectseismic tomographyen
dc.subjectmultiple right hand sidesen
dc.subjecttomographyen
dc.subjectSimulationen
dc.subjectfrequencyen
dc.subjectinversionen
dc.subjectmatrixen
dc.subjectdomainen
dc.subjectmathematics, applieden
dc.titleAn effective method for parameter estimation with pde constraints with multiple right-hand sidesen
dc.title.serialSiam Journal on Optimizationen
dc.typeArticle - Refereeden

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