Virginia TechHaber, EldadChung, MatthiasHerrmann, Felix2014-05-282014-05-282012Haber, 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: 10.1137/11081126x1052-6234http://hdl.handle.net/10919/48152Often, 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-USIn Copyrightpde constrained optimizationstochastic optimizationstochasticapproximationsample average approximationinverse problemsparameterestimationlarge scale problemsdc resistivityseismic tomographymultiple right hand sidestomographySimulationfrequencyinversionmatrixdomainmathematics, appliedArticle - Refereedhttp://epubs.siam.org/doi/abs/10.1137/11081126Xhttps://doi.org/10.1137/11081126x