期刊
SIAM JOURNAL ON SCIENTIFIC COMPUTING
卷 32, 期 5, 页码 2523-2542出版社
SIAM PUBLICATIONS
DOI: 10.1137/090775622
关键词
model reduction; statistical inverse problems; Markov chain Monte Carlo; optimization
资金
- Department of Energy [DE-FG02-08ER25858, DE-FG02-08ER25860]
- Singapore-MIT
- Air Force Office of Sponsored Research [FA9550-06-0271]
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.
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