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The challenge of quantifying uncertainty propagation in real-world systems is rooted in the high-dimensionality of the stochastic input and the frequent lack of explicit knowledge of its probability distribution.
The homogeneous chaos
N. Wiener · 1938
Earlier work this paper cites.
Environment and exposure to solvent of protein atoms. lysozyme and insulin
A. Shrake and J.A. Rupley · 1973
Earlier work this paper cites.
Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code
M. D. McKay, R. J. Beckman, and W. J. Conover · 1979
Earlier work this paper cites.
Comparison of simple potential functions for simulating liquid water
William L. Jorgensen, Jayaraman Chandrasekhar, Jeffry D. Madura, Roger W. Impey, and Michael L. Klein · 1983
Earlier work this paper cites.
Large sample properties of simulations using Latin Hypercube Sampling
M. Stein · 1987
Earlier work this paper cites.
Design and Analysis of Computer Experiments
Jerome Sacks, William J. Welch, Toby J. Mitchell, and Henry P. Wynn · 1989
Earlier work this paper cites.
Stochastic Finite Elements: A Spectral Approach
R. Ghanem and P. Spanos · 1991
Earlier work this paper cites.
Random number generation and Quasi-Monte Carlo methods
H. Niederreiter · 1992
Earlier work this paper cites.
The weighted histogram analysis method for free-energy calculations on biomolecules. i. the method
Shankar Kumar, John M. Rosenberg, Djamal Bouzida, Robert H. Swendsen, and Peter A. Kollman · 1992
Earlier work this paper cites.
A well-behaved electrostatic potential based method using charge restraints for deriving atomic charges: the resp model
Christopher I. Bayly, Piotr Cieplak, Wendy Cornell, and Peter A. Kollman · 1993
Earlier work this paper cites.
Sparse approximate solutions to linear systems
B. K. Natarajan · 1995
Earlier work this paper cites.
GROMACS: A message-passing parallel molecular dynamics implementation
H. J. C. Berendsen, D. van der Spoel, and R. van Drunen · 1995
Earlier work this paper cites.
Monte Carlo: Concepts, Algorithms, and Applications
G.S. Fishman · 1996
Earlier work this paper cites.
On Latin hypercube sampling
W.L. Loh · 1996
Earlier work this paper cites.
Monte Carlo and Quasi-Monte Carlo methods 1996
H. Niederreiter, P. Hellekalek, G. Larcher, and P. Zinterhof · 1998
Earlier work this paper cites.
Lincs: A linear constraint solver for molecular simulations
Berk Hess, Henk Bekker, J. C. Berendsen Herman, and G. E. M. Fraaije Johannes · 1998
Earlier work this paper cites.
Strategies for Quasi-Monte Carlo
B.L. Fox · 1999
Earlier work this paper cites.
Multilevel Monte Carlo Methods
Stefan Heinrich · 2001
Earlier work this paper cites.
Bayesian calibration of computer models
Marc C. Kennedy and Anthony O’Hagan · 2001
Earlier work this paper cites.
Uncertainty Quantification with Experimental Data and Complex System Models
Trent Michael Russi · 2001
Earlier work this paper cites.
Anisotropy of fluctuation dynamics of proteins with an elastic network model
A. R. Atilgan, S. R. Durell, R. L. Jernigan, M. C. Demirel, O. Keskin, and I. Bahar · 2001
Earlier work this paper cites.
Electrostatics of nanosystems: application to microtubules and the ribosome
Nathan A Baker, David Sept, Simpson Joseph, Michael J Holst, and J Andrew McCammon · 2001
Earlier work this paper cites.
Escaping free-energy minima
Alessandro Laio and Michele Parrinello · 2002
Earlier work this paper cites.
The wiener-askey polynomial chaos for stochastic differential equations
D. Xiu and G. E. Karniadakis · 2002
Earlier work this paper cites.
Bayesian inference for the uncertainty distribution of computer model outputs
Jeremy Oakley and Anthony O’Hagan · 2002
Earlier work this paper cites.
Spectral polynomial chaos solutions of the stochastic advection equation
M Jardak, Chau-Hsing Su, and George Em Karniadakis · 2002
Earlier work this paper cites.
Modeling uncertainty in flow simulations via generalized polynomial chaos
D. Xiu and G.E. Karniadakis · 2003
Earlier work this paper cites.
A stochastic collocation algorithm for uncertainty analysis
L. Mathelin and M.Y. Hussaini · 2003
Earlier work this paper cites.
Development and testing of a general amber force field
Junmei Wang, Romain M. Wolf, James W. Caldwell, Peter A. Kollman, and David A. Case · 2004
Earlier work this paper cites.
Settle: An analytical version of the shake and rattle algorithm for rigid water models
Shuichi Miyamoto and A. Kollman Peter · 2004
Earlier work this paper cites.
Identification and prediction of stochastic dynamical systems in a polynomial chaos basis
R. Ghanem, S. Masri, M. Pellissetti, and R. Wolfe · 2005
Earlier work this paper cites.
High-order collocation methods for differential equations with random inputs
D. Xiu and J.S. Hesthaven · 2005
Earlier work this paper cites.
Lectures on Statistical Physics and Protein Folding
Kerson Huang · 2005
Earlier work this paper cites.
Error correction via linear programming
E. Candès, M. Rudelson, T. Tao, and R. Vershynin · 2005
Earlier work this paper cites.
Decoding by linear programming
E. J. Candès and T. Tao · 2005
Earlier work this paper cites.
Biomolecular Applications of Poisson?Boltzmann Methods
Nathan A. Baker · 2005
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Uncertainty propagation in CFD using polynomial chaos decomposition
O.M. Knio and O.P. Le Maitre · 2006
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Multi-element generalized polynomial chaos for arbitrary probability measures
X. Wan and G.E. Karniadakis · 2006
Reweighted ℓ 1 \ell_{1} minimization method for stochastic elliptic differential equations
X. Yang and G. E. Karniadakis · 2013
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Paul G Constantine, Eric Dow, and Qiqi Wang · 2014
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D. Donoho, M. Elad, and V. Temlyakov · 2006
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E. J. Candès, J. Romberg, and T. Tao · 2006
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A stochastic collocation method for elliptic partial differential equations with random input data
Ivo Babu s ˇ \check{\rm{s}} ka, Fabio Nobile, and Ra u ´ \acute{\rm{u}} l Tempone · 2007
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Spgl1: A solver for large-scale sparse reconstruction
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Y. L. Liu and L. Guo · 2016
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Spacecraft uncertainty propagation using gaussian mixture models and polynomial chaos expansions
Vivek Vittaldev, Ryan P. Russell, and Richard Linares · 2016
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R. Ahlfeld, B. Belkouchi, and F. Montomoli · 2016
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X. Yang, H. Lei, N. A. Baker, and G. Lin · 2016
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Statistical Framework for Uncertainty Quantification in Computational Molecular Modeling
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A Continuation Multi Level Monte Carlo (C-MLMC) method for uncertainty quantification in compressible inviscid aerodynamics
M. Pisaroni, F. Nobile, and P. Leyland · 2017
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Comparison of Surrogate-Based Uncertainty Quantification Methods for Computationally Expensive Simulators
N. Owen, P. Challenor, P. Menon, and S. Bennani · 2017
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Sparse approximation using ℓ 1 − ℓ 2 \ell_{1}-\ell_{2} minimization and its application to stochastic collocation
Liang Yan, Yeonjong Shin, and Dongbin Xiu · 2017
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Systematic parameter inference in stochastic mesoscopic modeling
H. Lei, X. Yang, Z. Li, and G. E. Karniadakis · 2017
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Divide and conquer: An incremental sparsity promoting compressive sampling approach for polynomial chaos expansions
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A general framework of enhancing sparsity of generalized polynomial chaos expansions, 2017
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