Large-scale inverse model analyses employing fast randomized data reduction: INVERSE MODELING WITH DATA REDUCTION

Journal Article · Thu Jul 06 00:00:00 EDT 2017 · Water Resources Research

DOI:https://doi.org/10.1002/2016WR020299· OSTI ID:1507327

Lin, Youzuo  ^[1]; Le, Ellen B.  ^[2]; O'Malley, Daniel  ^[1]; Vesselinov, Velimir V.  ^[1]; Bui-Thanh, Tan ^[2]

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1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2. Univ. of Texas, Austin, TX (United States)

When the number of observations is large, it is computationally challenging to apply classical inverse modeling techniques. We have developed a new computationally efficient technique for solving inverse problems with a large number of observations (e.g., on the order of 10⁷ or greater). Our method, which we call the randomized geostatistical approach (RGA), is built upon the principal component geostatistical approach (PCGA). We employ a data reduction technique combined with the PCGA to improve the computational efficiency and reduce the memory usage. Specifically, we employ a randomized numerical linear algebra technique based on a so-called “sketching” matrix to effectively reduce the dimension of the observations without losing the information content needed for the inverse analysis. In this way, the computational and memory costs for RGA scale with the information content rather than the size of the calibration data. Our algorithm is coded in Julia and implemented in the MADS open-source high-performance computational framework (http://mads.lanl.gov). We apply our new inverse modeling method to invert for a synthetic transmissivity field. Compared to a standard geostatistical approach (GA), our method is more efficient when the number of observations is large. Moreover, our method is capable of solving larger inverse problems than the standard GA and PCGA approaches. Thus, our new model inversion method is a powerful tool for solving large-scale inverse problems. The method can be applied in any field and is not limited to hydrogeological applications such as the characterization of aquifer heterogeneity.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• Grant/Contract Number: 89233218CNA000001; SC11145687; 11145687
• OSTI ID: 1507327
• Alternate ID(s): OSTI ID: 1374898
• Report Number(s): LA-UR-17-20239
• Journal Information: Water Resources Research, Vol. 53, Issue 8; ISSN 0043-1397
• Publisher: American Geophysical Union (AGU)
• Country of Publication: United States
• Language: English

Related Subjects

54 ENVIRONMENTAL SCIENCES
97 MATHEMATICS AND COMPUTING
hydraulic inverse modeling
data reduction
randomization
geostatistical inversion