The DOI matches its Crossref record; 53 of the 53 references it cites were found in a registry or an index.
Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems
Open accessAbstract
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.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Equation of State Calculations by Fast Computing Machines
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953) · The Journal of Chemical Physics · doi:10.1063/1.1699114 · Cited by 37,192
Monte Carlo sampling methods using Markov chains and their applications.
Hastings, W. K. (1970) · Biometrika · doi:10.1093/biomet/57.1.97 · Cited by 15,195
On the limited memory BFGS method for large scale optimization
Liu, D. C., & Nocedal, J. (1989) · Mathematical Programming · doi:10.1007/bf01589116 · Cited by 8,560
Sampling-based approaches to calculating marginal densities
Gelfand, A. E., & Smith, A. F. M. (1990) · Journal of the American Statistical Association · doi:10.1080/01621459.1990.10476213 · Cited by 6,606
Inverse Problem Theory and Methods for Model Parameter Estimation
Tarantola, A. (2005) · doi:10.1137/1.9780898717921 · Cited by 6,585
Turbulence and the dynamics of coherent structures. I. Coherent structures
Sirovich, L. (1987) · Quarterly of Applied Mathematics · doi:10.1090/qam/910462 · Cited by 6,224
Principal component analysis in linear systems: Controllability, observability, and model reduction
Moore, B. (1981) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1981.1102568 · Cited by 5,282
Regularization of Inverse Problems
Engl, H. W., Hanke, M., & Neubauer, A. (1996) · Springer eBooks · doi:10.1007/978-94-009-1740-8 · Cited by 5,275
Bayesian calibration of computer models
Kennedy, M. C., & O'Hagan, A. (2001) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/1467-9868.00294 · Cited by 4,222
Gelman, A. (2006) · Bayesian Analysis · doi:10.1214/06-ba117a · Cited by 4,050
Cited by
A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
Benner, P., Gugercin, S., & Willcox, K. (2015) · SIAM Review · doi:10.1137/130932715 · Cited by 1,916
Self-citationActive Subspace Methods in Theory and Practice: Applications to Kriging Surfaces
Constantine, P. G., Dow, E., & Wang, Q. (2014) · SIAM Journal on Scientific Computing · doi:10.1137/130916138 · Cited by 506
Yondo, R., Andrés, E., & Valero, E. (2018) · Progress in Aerospace Sciences · doi:10.1016/j.paerosci.2017.11.003 · Cited by 311
Metadata
- Authors
- Lieberman, C., Willcox, K., & Ghattas, O.
- Venue
- SIAM Journal on Scientific Computing
- Published
- 2010-01
- Volume
- 32
- Issue
- 5
- Pages
- 2523-2542
- ISSN
- 1064-8275 (ISSN-L)
- 1095-7197
- OpenAlex
- W2075385817
- Cited by
- 254
- References
- 53
- FWCI
- 9.01
- Type
- journal article
- Language
- en
- Open access
- green
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems. https://app.cochat.ai/papers/10.1137/090775622
- The paper
- Lieberman, C., Willcox, K., & Ghattas, O. (2010). Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems. SIAM Journal on Scientific Computing. https://doi.org/10.1137/090775622
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
