Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems
Name
Lieberman-2010-PARAMETER AND STATE.pdf
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804.38 KB
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Adobe PDF
Checksum (MD5)
299b2eebec02d086ec32f0cb7c3ac03f
Author(s)
Lieberman, Chad E.
Willcox, Karen E.
Ghattas, O.
Date Issued
August 2010
Journal
SIAM Journal on Scientific Computing
Publisher
Society of Industrial and Applied Mathematics (SIAM)
Citation
Lieberman, Chad, Karen Willcox, and Omar Ghattas. “Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems.” SIAM Journal on Scientific Computing 32.5 (2010): 2523-2542. © 2010 SIAM
Version
Final published version
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Aerospace Controls Laboratory
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1137/090775622
