{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,4]],"date-time":"2026-09-04T23:00:47Z","timestamp":1788562847685,"version":"build-2803163510"},"reference-count":37,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>A greedy algorithm for the construction of a reduced model with reduction in both parameter and state is developed for an efficient solution of statistical inverse problems governed by partial differential equations with distributed parameters. Large-scale models are too costly to evaluate repeatedly, as is required in the statistical setting. Furthermore, these models often have high-dimensional parametric input spaces, which compounds the difficulty of effectively exploring the uncertainty space. We simultaneously address both challenges by constructing a projection-based reduced model that accepts low-dimensional parameter inputs and whose model evaluations are inexpensive. The associated parameter and state bases are obtained through a greedy procedure that targets the governing equations, model outputs, and prior information. The methodology and results are presented for groundwater inverse problems in one and two dimensions.<\/jats:p>","DOI":"10.1137\/090775622","type":"journal-article","created":{"date-parts":[[2010,8,20]],"date-time":"2010-08-20T18:48:15Z","timestamp":1282330095000},"page":"2523-2542","source":"Crossref","is-referenced-by-count":195,"title":["Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems"],"prefix":"10.1137","volume":"32","author":[{"given":"Chad","family":"Lieberman","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Karen","family":"Willcox","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Omar","family":"Ghattas","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,8,19]]},"reference":[{"key":"R1","unstructured":"V. Akcelik, G. Biros, O. Ghattas, J. 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