An effective method for parameter estimation with pde constraints with multiple right-hand sides
dc.contributor | Virginia Tech | en |
dc.contributor.author | Haber, Eldad | en |
dc.contributor.author | Chung, Matthias | en |
dc.contributor.author | Herrmann, Felix | en |
dc.contributor.department | Mathematics | en |
dc.date.accessed | 2014-05-27 | en |
dc.date.accessioned | 2014-05-28T18:35:07Z | en |
dc.date.available | 2014-05-28T18:35:07Z | en |
dc.date.issued | 2012 | en |
dc.description.abstract | 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. | en |
dc.description.sponsorship | NSERC IRC program | en |
dc.description.sponsorship | Texas State University Research Enhancement Program | en |
dc.identifier.citation | Haber, 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: 10.1137/11081126x | en |
dc.identifier.doi | https://doi.org/10.1137/11081126x | en |
dc.identifier.issn | 1052-6234 | en |
dc.identifier.uri | http://hdl.handle.net/10919/48152 | en |
dc.identifier.url | http://epubs.siam.org/doi/abs/10.1137/11081126X | en |
dc.language.iso | en_US | en |
dc.publisher | Siam Publications | en |
dc.rights | In Copyright | en |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
dc.subject | pde constrained optimization | en |
dc.subject | stochastic optimization | en |
dc.subject | stochastic | en |
dc.subject | approximation | en |
dc.subject | sample average approximation | en |
dc.subject | inverse problems | en |
dc.subject | parameter | en |
dc.subject | estimation | en |
dc.subject | large scale problems | en |
dc.subject | dc resistivity | en |
dc.subject | seismic tomography | en |
dc.subject | multiple right hand sides | en |
dc.subject | tomography | en |
dc.subject | Simulation | en |
dc.subject | frequency | en |
dc.subject | inversion | en |
dc.subject | matrix | en |
dc.subject | domain | en |
dc.subject | mathematics, applied | en |
dc.title | An effective method for parameter estimation with pde constraints with multiple right-hand sides | en |
dc.title.serial | Siam Journal on Optimization | en |
dc.type | Article - Refereed | en |
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