The DOI matches its Crossref record; 13 of the 13 references it cites were found in a registry or an index.
Active Subspace Methods in Theory and Practice: Applications to Kriging Surfaces
Open accessAbstract
Many multivariate functions in engineering models vary primarily along a few directions in the space of input parameters. When these directions correspond to coordinate directions, one may apply global sensitivity measures to determine the most influential parameters. However, these methods perform poorly when the directions of variability are not aligned with the natural coordinates of the input space. We present a method to first detect the directions of the strongest variability using evaluations of the gradient and subsequently exploit these directions to construct a response surface on a low-dimensional subspace---i.e., the active subspace---of the inputs. We develop a theoretical framework with error bounds, and we link the theoretical quantities to the parameters of a kriging response surface on the active subspace. We apply the method to an elliptic PDE model with coefficients parameterized by 100 Gaussian random variables and compare it with a local sensitivity analysis method for dimension reduction.
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
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
A Singular Value Thresholding Algorithm for Matrix Completion
Cai, J.-F., Candès, E. J., & Shen, Z. (2010) · SIAM Journal on Optimization · doi:10.1137/080738970 · Cited by 5,809
Understanding the Metropolis-Hastings Algorithm
Chib, S., & Greenberg, E. (1995) · The American Statistician · doi:10.1080/00031305.1995.10476177 · Cited by 4,145
Halko, N., Martinsson, P. G., & Tropp, J. A. (2011) · SIAM Review · doi:10.1137/090771806 · Cited by 4,002
A Taxonomy of Global Optimization Methods Based on Response Surfaces
Jones, D. R. (2001) · Journal of Global Optimization · doi:10.1023/a:1012771025575 · Cited by 2,159
Aerodynamic design via control theory
Jameson, A. (1988) · Journal of Scientific Computing · doi:10.1007/bf01061285 · Cited by 1,930
A Simple Mesh Generator in MATLAB
Persson, P.-O., & Strang, G. (2004) · SIAM Review · doi:10.1137/s0036144503429121 · Cited by 1,552
Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations
Babuska, I. M., Tempone, R. F., & Zouraris, G. E. (2004) · SIAM Journal on Numerical Analysis · doi:10.1137/s0036142902418680 · Cited by 877
Stochastic spectral methods for efficient Bayesian solution of inverse problems
Marzouk, Y. M., Najm, H. N., & Rahn, L. A. (2007) · Journal of Computational Physics · doi:10.1016/j.jcp.2006.10.010 · Cited by 470
Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems
Lieberman, C., Willcox, K., & Ghattas, O. (2010) · SIAM Journal on Scientific Computing · doi:10.1137/090775622 · Cited by 254
Cited by
Yondo, R., Andrés, E., & Valero, E. (2018) · Progress in Aerospace Sciences · doi:10.1016/j.paerosci.2017.11.003 · Cited by 311
Xiao, H., Wu, J.-L., Wang, J.-X., Sun, R., & Roy, C. J. (2016) · Journal of Computational Physics · doi:10.1016/j.jcp.2016.07.038 · Cited by 304
Preston, S. P., Wilkinson, R. D., Clayton, R. H., Chappell, M. J., & Mirams, G. R. (2025) · Current Opinion in Systems Biology · doi:10.1016/j.coisb.2025.100563 · Cited by 11
Metadata
- Authors
- Constantine, P. G., Dow, E., & Wang, Q.
- Venue
- SIAM Journal on Scientific Computing
- Published
- 2014-01
- Volume
- 36
- Issue
- 4
- Pages
- A1500-A1524
- ISSN
- 1064-8275 (ISSN-L)
- 1095-7197
- OpenAlex
- W2053469438
- Cited by
- 506
- References
- 13
- FWCI
- 10.55
- 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: Active Subspace Methods in Theory and Practice: Applications to Kriging Surfaces. https://app.cochat.ai/papers/10.1137/130916138
- The paper
- Constantine, P. G., Dow, E., & Wang, Q. (2014). Active Subspace Methods in Theory and Practice: Applications to Kriging Surfaces. SIAM Journal on Scientific Computing. https://doi.org/10.1137/130916138
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.
