Reduced Wiener Chaos representation of random fields via basis adaptation and projection

Arnst, 2010, Identification of bayesian posteriors for coefficients of chaos expansions, J. Comput. Phys., 229, 3134, 10.1016/j.jcp.2009.12.033

Cameron, 1947, The orthogonal development of nonlinear functionals in series of Fourier–Hermite functionals, Ann. Math., 48, 385, 10.2307/1969178

Das, 2008, Asymptotic sampling distribution for polynomial chaos representation from data: a maximum entropy and Fisher information approach, SIAM J. Sci. Comput., 30, 2207, 10.1137/060652105

Desceliers, 2006, Maximum likelihood estimation of stochastic chaos representations from experimental data, Int. J. Numer. Methods Eng., 66, 978, 10.1002/nme.1576

Doostan, 2009, A least-squares approximation of partial differential equations with high-dimensional random inputs, J. Comput. Phys., 228, 4332, 10.1016/j.jcp.2009.03.006

Doostan, 2011, A non-adapted sparse approximation of pdes with stochastic inputs, J. Comput. Phys., 230, 3015, 10.1016/j.jcp.2011.01.002

Ghanem, 1999, Ingredients for a general purpose stochastic finite elements implementation, Comput. Methods Appl. Mech. Eng., 168, 19, 10.1016/S0045-7825(98)00106-6

Ghanem, 1998, Stochastic finite element analysis for multiphase flow in heterogeneous porous media, Transp. Porous Media, 32, 239, 10.1023/A:1006514109327

Ghanem, 2006, Characterization of stochastic system parameters from experimental data: a bayesian inference approach, J. Comput. Phys., 217, 63, 10.1016/j.jcp.2006.01.037

Ghanem, 1999, Propagation of probabilistic uncertainty in complex physical systems using a stochastic finite element approach, Physica D, 133, 137, 10.1016/S0167-2789(99)00102-5

Ghanem, 2008, A probabilistic construction of model validation, Comput. Methods Appl. Mech. Eng., 197, 2585, 10.1016/j.cma.2007.08.029

Huan, 2013, Simulation-based optimal bayesian experimental design for nonlinear systems, J. Comput. Phys., 232, 288, 10.1016/j.jcp.2012.08.013

Le Maître, 2002, A stochastic projection method for fluid flow: II. Random process, J. Comput. Phys., 181, 9, 10.1006/jcph.2002.7104

Marzouk, 2007, Stochastic spectral methods for efficient bayesian solution of inverse problems, J. Comput. Phys., 224, 560, 10.1016/j.jcp.2006.10.010

Marzouk, 2009, Dimensionality reduction and polynomial chaos acceleration of bayesian inference in inverse problems, J. Comput. Phys., 228, 1862, 10.1016/j.jcp.2008.11.024

Matthies, 1999, Finite elements for stochastic media problems, Comput. Methods Appl. Mech. Eng., 168, 3, 10.1016/S0045-7825(98)00100-5

Mercer, 1909, Functions of positive and negative type, and their connection with the theory of integral equations, Philos. Trans. R. Soc. Lond. Ser. A, 209, 415, 10.1098/rsta.1909.0016

Najm, 2009, Uncertainty quantification and polynomial chaos techniques in computational fluid dynamics, Annu. Rev. Fluid Mech., 41, 35, 10.1146/annurev.fluid.010908.165248

Reagana, 2003, Uncertainty quantification in reacting-flow simulations through non-intrusive spectral projection, Combust. Flame, 132, 545, 10.1016/S0010-2180(02)00503-5

Saad, 2009, Characterization of reservoir simulation models using a polynomial chaos-based ensemble Kalman filter, Water Resour. Res., 45, 10.1029/2008WR007148

Soize, 2009, Reduced chaos decomposition with random coefficients of vector-valued random variables and random fields, Comput. Methods Appl. Mech. Eng., 198, 1926, 10.1016/j.cma.2008.12.035

Tipireddy, 2014, Basis adaptation in homogeneous chaos spaces, J. Comput. Phys., 259, 304, 10.1016/j.jcp.2013.12.009

Tsilifis, 2017, Reduced-dimensionality Legendre chaos expansions via basis adaptation on 1d active subspaces, ASME J. Verification, Valid. Uncertain. Quantification

Wick, 1950, The evaluation of the collision matrix, Phys. Rev., 80, 268, 10.1103/PhysRev.80.268

Wiener, 1938, The homogeneous chaos, Am. J. Math., 60, 897, 10.2307/2371268

Xiu, 2003, Modeling uncertainty in flow simulations via generalized polynomial chaos, J. Comput. Phys., 187, 137, 10.1016/S0021-9991(03)00092-5