An adaptive ANOVA-based PCKF for high-dimensional nonlinear inverse modeling
Tài liệu tham khảo
Metropolis, 1953, Equation of state calculations by fast computing machines, J. Chem. Phys., 21, 1087, 10.1063/1.1699114
Geman, 1984, Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images, IEEE Trans. Pattern Anal. Mach. Intell., PAMI-6, 721, 10.1109/TPAMI.1984.4767596
Kalman, 1960, A new approach to linear filtering and prediction problems, J. Basic Eng., 82, 35, 10.1115/1.3662552
Evensen, 1994, Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics, J. Geophys. Res., Oceans, 99, 10143, 10.1029/94JC00572
Evensen, 2009
Evensen, 2003, The ensemble Kalman filter: theoretical formulation and practical implementation, Ocean Dyn., 53, 343, 10.1007/s10236-003-0036-9
Wiener, 1938, The homogeneous chaos, Am. J. Math., 60, 897, 10.2307/2371268
Ghanem, 2003
Xiu, 2003, Modeling uncertainty in flow simulations via generalized polynomial chaos, J. Comput. Phys., 187, 137, 10.1016/S0021-9991(03)00092-5
Isukapalli, 1998, Stochastic response surface methods (SRSMs) for uncertainty propagation: application to environmental and biological systems, Risk Anal., 18, 351, 10.1111/j.1539-6924.1998.tb01301.x
Tatang, 1997, An efficient method for parametric uncertainty analysis of numerical geophysical models, J. Geophys. Res., 102, 21925, 10.1029/97JD01654
Xiu, 2005, High-order collocation methods for differential equations with random inputs, SIAM J. Sci. Comput., 27, 1118, 10.1137/040615201
Eldred, 2009, Comparison of non-intrusive polynomial chaos and stochastic collocation methods for uncertainty quantification
Webster, 1996
Hockenberry, 2004, Evaluation of uncertainty in dynamic simulations of power system models: The probabilistic collocation method, IEEE Trans. Power Syst., 19, 1483, 10.1109/TPWRS.2004.831689
Li, 2007, Probabilistic collocation method for flow in porous media: Comparisons with other stochastic methods, Water Resour. Res., 43, 10.1029/2006WR005673
Li, 2009, Stochastic analysis of unsaturated flow with probabilistic collocation method, Water Resour. Res., 45, 10.1029/2008WR007530
Saad, 2009, Characterization of reservoir simulation models using a polynomial chaos-based ensemble Kalman filter, Water Resour. Res., 45, 10.1029/2008WR007148
Li, 2009, A generalized polynomial chaos based ensemble Kalman filter with high accuracy, J. Comput. Phys., 228, 5454, 10.1016/j.jcp.2009.04.029
Zeng, 2010, A stochastic collocation based Kalman filter for data assimilation, Comput. Geosci., 14, 721, 10.1007/s10596-010-9183-5
Zeng, 2011, A probabilistic collocation-based Kalman filter for history matching, SPE J., 16, 294, 10.2118/140737-PA
Li, 2011, Probabilistic collocation based Kalman filter for assisted history matching—a case study, 10.2118/141930-MS
Rabitz, 1999, General foundations of high-dimensional model representations, J. Math. Chem., 25, 197, 10.1023/A:1019188517934
Li, 2001, High dimensional model representations generated from low dimensional data samples. I. mp-Cut-HDMR, J. Math. Chem., 30, 1, 10.1023/A:1013172329778
Foo, 2010, Multi-element probabilistic collocation method in high dimensions, J. Comput. Phys., 229, 1536, 10.1016/j.jcp.2009.10.043
Ma, 2010, An adaptive high-dimensional stochastic model representation technique for the solution of stochastic partial differential equations, J. Comput. Phys., 229, 3884, 10.1016/j.jcp.2010.01.033
Yang, 2012, Adaptive ANOVA decomposition of stochastic incompressible and compressible flows, J. Comput. Phys., 231, 1587, 10.1016/j.jcp.2011.10.028
Burgers, 1998, Analysis scheme in the ensemble Kalman filter, Mon. Weather Rev., 126, 1719, 10.1175/1520-0493(1998)126<1719:ASITEK>2.0.CO;2
Whitaker, 2002, Ensemble data assimilation without perturbed observations, Mon. Weather Rev., 130, 1913, 10.1175/1520-0493(2002)130<1913:EDAWPO>2.0.CO;2