357
Views
9
CrossRef citations to date
0
Altmetric
Section B

Proper orthogonal decompositions in multifidelity uncertainty quantification of complex simulation models

, &
Pages 748-769 | Received 31 Jan 2013, Accepted 29 Aug 2013, Published online: 20 Jan 2014

References

  • M. Alexe, O. Roderick, M. Anitescu, J. Utke, T. Fanning, and P. Hovland, Using automatic differentiation in sensitivity analysis of nuclear simulation models, Trans. Amer. Nucl. Soc. 102 (2010), pp. 235–237.
  • M. Anitescu, J. Chen, and L. Wang, A matrix-free approach for solving the parametric Gaussian process maximum likelihood problem, SIAM J. Sci. Comput. 34 (2012), pp. A240–A262. Available at http://epubs.siam.org/doi/abs/10.1137/110831143. doi: 10.1137/110831143
  • O.G.T. Bui-Thanh and K. Willcox, Model reduction for large-scale systems with high-dimensional parametric input space, SIAM J. Sci. Comput. 30(6) (2008), pp. 3270–3288. doi: 10.1137/070694855
  • N. Cressie, Spatial prediction and ordinary kriging, Math. Geol. 20(4) (1988), pp. 405–421. doi: 10.1007/BF00892986
  • N. Cressie, Statistics for Spatial Data, Wiley Series in Probability and Mathematical Statistics. Applied Probability and Statistics Section, John Wiley & Sons, New York, 1993.
  • D.N. Daescu and I.M. Navon, A dual-weighted approach to order reduction in 4D-var data assimilation, Mon. Weather Rev. 136(3) (2008), pp. 1026–1041. doi: 10.1175/2007MWR2102.1
  • A. DasGupta, Asymptotic Theory of Statistics and Probability, Springer, New York, 2008.
  • J.L. Doob, Stochastic Processes, Vol. 101, John Wiley & Sons, New York, 1953.
  • J. Duderstadt and L. Hamilton, Nuclear Reactor Analysis, Wiley, New York, 1976.
  • P. Fischer, Nek5000-open source spectral element cfd solver, 2008. Available at https://nek5000.mcs.anl.gov/index.php/MainPage.
  • M. Frangos, B.v.B. Waanders, and Y. Marzouk, Surrogate and Reduced-order Modeling: A Comparison of Approaches for Large-scale Statistical Inverse Problems, John Wiley & Sons, New York, 2011, pp. 123–150.
  • K.W.O.G.D. Galbally and K. Fidskowski, Non-linear model reduction for uncertainty quantification in large-scale inverse problems, Int. J. Numer. Methods Eng. 81 (2010), pp. 1581–1608.
  • M. Gunzburger, Reduced-order modeling, data compression and the design of experiments, Second DOE Workshop of Multiscale Mathematics, Bromfield, CO, 2004.
  • M. Hinze and S. Volkwein, Proper Orthogonal Decomposition Surrogate Models for Nonlinear Dynamical Systems: Error Estimates and Suboptimal Control, Lecture Notes in Computational Science and Engineering, Vol. 45, Springer, New York, 2005.
  • L.P.C. Homescu and R. Serban, Error estimation for reduced order models of dynamical systems, Tech. Rep., United States, Department of Energy, 2003.
  • M. Kennedy and A. O'Hagan, Predicting the output from a complex computer code when fast approximations are available, Biometrika 87 (2000), pp. 1–13. doi: 10.1093/biomet/87.1.1
  • M. Kennedy and A. O'Hagan, Bayesian calibration of computer models, J. R. Stat. Soc. Ser. B Stat. Methodol. 63 (2001), pp. 425–464. doi: 10.1111/1467-9868.00294
  • C. Kenney and A. Laub, Small-sample statistical condition estimates for general matrix functions, SIAM J. Sci. Comput. 15(1) (1994), pp. 36–61. doi: 10.1137/0915003
  • D.C.Y. Lacouture, How to use matlab to fit the ex-gaussian and other probability functions to a distribution of response times, Tutorials Quant. Methods Psychol. 4(1) (2008), pp. 35–45.
  • O.G.C. Lieberman and K. Willcox, Parameter and state model reduction for large-scale statistical inverse problems, SIAM J. Sci. Comput. 32 (2010), pp. 2523–2542. doi: 10.1137/090775622
  • B.A. Lockwood and M. Anitescu, Gradient-enhanced universal kriging for uncertainty propagation, Nucl. Sci. Eng. 170(2) (2012), pp. 168–195.
  • E. Merzari, P. Fischer, and D. Pointer, A POD-based Solver for the Advection-Diffusion Equation, Proceeding of ASME-JSME, KSME Joint Fluids Engineering Conference, Hamamatsu, Shizuoka, Japan, 2011.
  • C. Rasmussen and C. Williams, Gaussian Processes for Machine Learning, MIT Press, Cambridge, MA, 2006.
  • O. Roderick, Model reduction for simulation, optimization and control, Ph.D. thesis, Portland State University, 2009.
  • O. Roderick, M. Anitescu, and P. Fischer, Polynomial regression approaches using derivative information for uncertainty quantification, Nucl. Sci. Eng. 164 (2) (2010), pp. 122–139.
  • M. Stein, Interpolation of Spatial Data: Some Theory for Kriging, Springer-Verlag, Berlin, 1999.
  • S. Volkwein, Proper orthogonal decomposition: Applications in optimization and control, CEA-EDF-INRIA Numerical Analysis Summer School, Cadarache, France, 2007.
  • L.S.G. Webber and R. Handler, The Karhunen-Loeve decomposition of minimal channel flow, Phys. Fluids 9 (1997), pp. 1054–1066. doi: 10.1063/1.869323

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.