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All issues ESAIM: M2AN, 46 2 (2012) 317-339 Article references

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Journal of Mathematical Analysis and Applications 454 (1) 303 (2017)
DOI: 10.1016/j.jmaa.2017.04.062
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An efficient method for stochastic optimal control with joint chance constraints for nonlinear systems

Joel A. Paulson and Ali Mesbah
International Journal of Robust and Nonlinear Control 29 (15) 5017 (2019)
DOI: 10.1002/rnc.3999
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Handbook of Uncertainty Quantification

Christian Soize
Handbook of Uncertainty Quantification 883 (2017)
DOI: 10.1007/978-3-319-12385-1_30
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Handbook of Uncertainty Quantification

Bert Debusschere
Handbook of Uncertainty Quantification 617 (2017)
DOI: 10.1007/978-3-319-12385-1_19
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Handbook of Uncertainty Quantification

Khachik Sargsyan
Handbook of Uncertainty Quantification 673 (2017)
DOI: 10.1007/978-3-319-12385-1_22
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Conformally mapped polynomial chaos expansions for Maxwell's source problem with random input data

Niklas Georg and Ulrich Römer
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 33 (6) e2776 (2020)
DOI: 10.1002/jnm.2776
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Efficient uncertainty quantification in fully-integrated surface and subsurface hydrologic simulations

K.L. Miller, S.J. Berg, J.H. Davison, E.A. Sudicky and P.A. Forsyth
Advances in Water Resources 111 381 (2018)
DOI: 10.1016/j.advwatres.2017.10.023
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Convergence of a method based on the exponential integrator and Fourier spectral discretization for stiff stochastic PDEs

Zohreh Asgari and S. Mohammad Hosseini
Mathematical Methods in the Applied Sciences 41 (17) 8294 (2018)
DOI: 10.1002/mma.5290
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Progress in Industrial Mathematics at ECMI 2012

E. Jan W. ter Maten, Roland Pulch, Wil H. A. Schilders and H. H. J. M. Janssen
Mathematics in Industry, Progress in Industrial Mathematics at ECMI 2012 19 361 (2014)
DOI: 10.1007/978-3-319-05365-3_50
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Robust Information Divergences for Model-Form Uncertainty Arising from Sparse Data in Random PDE

Eric Joseph Hall and Markos A. Katsoulakis
SIAM/ASA Journal on Uncertainty Quantification 6 (4) 1364 (2018)
DOI: 10.1137/17M1143344
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A Single Formulation for Uncertainty Propagation in Turbomachinery: SAMBA PC

Richard Ahlfeld and Francesco Montomoli
Journal of Turbomachinery 139 (11) 111007 (2017)
DOI: 10.1115/1.4037362
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Stochastic model reduction for polynomial chaos expansion of acoustic waves using proper orthogonal decomposition

Nabil El Moçayd, M. Shadi Mohamed, Driss Ouazar and Mohammed Seaid
Reliability Engineering & System Safety 195 106733 (2020)
DOI: 10.1016/j.ress.2019.106733
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Optimal Partition in Terms of Independent Random Vectors of Any Non-Gaussian Vector Defined by a Set of Realizations

C. Soize
SIAM/ASA Journal on Uncertainty Quantification 5 (1) 176 (2017)
DOI: 10.1137/16M1062223
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Polynomial Chaos Expansions for the Stability Analysis of Uncertain Delay Differential Equations

Rossana Vermiglio
SIAM/ASA Journal on Uncertainty Quantification 5 (1) 278 (2017)
DOI: 10.1137/15M1029618
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Effectively Subsampled Quadratures for Least Squares Polynomial Approximations

Pranay Seshadri, Akil Narayan and Sankaran Mahadevan
SIAM/ASA Journal on Uncertainty Quantification 5 (1) 1003 (2017)
DOI: 10.1137/16M1057668
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A Generalized Sampling and Preconditioning Scheme for Sparse Approximation of Polynomial Chaos Expansions

John D. Jakeman, Akil Narayan and Tao Zhou
SIAM Journal on Scientific Computing 39 (3) A1114 (2017)
DOI: 10.1137/16M1063885
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Nonlinear Model Predictive Control with Explicit Backoffs for Stochastic Systems under Arbitrary Uncertainty

Joel A. Paulson and Ali Mesbah
IFAC-PapersOnLine 51 (20) 523 (2018)
DOI: 10.1016/j.ifacol.2018.11.036
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On the performance evaluation of stochastic finite elements in linear and nonlinear problems

Nan Feng, Guodong Zhang and Kapil Khandelwal
Computers & Structures 243 106408 (2021)
DOI: 10.1016/j.compstruc.2020.106408
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Sliced-Inverse-Regression--Aided Rotated Compressive Sensing Method for Uncertainty Quantification

Xiu Yang, Weixuan Li and Alexandre Tartakovsky
SIAM/ASA Journal on Uncertainty Quantification 6 (4) 1532 (2018)
DOI: 10.1137/17M1148955
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Uncertainty quantification for nonlinear difference equations with dependent random inputs via a stochastic Galerkin projection technique

J. Calatayud, J.-C. Cortés and M. Jornet
Communications in Nonlinear Science and Numerical Simulation 72 108 (2019)
DOI: 10.1016/j.cnsns.2018.12.011
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Data-driven polynomial chaos expansions: A weighted least-square approximation

Ling Guo, Yongle Liu and Tao Zhou
Journal of Computational Physics 381 129 (2019)
DOI: 10.1016/j.jcp.2018.12.020
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Optimal Bayesian experiment design for nonlinear dynamic systems with chance constraints

Joel A. Paulson, Marc Martin-Casas and Ali Mesbah
Journal of Process Control 77 155 (2019)
DOI: 10.1016/j.jprocont.2019.01.010
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A general framework for data-driven uncertainty quantification under complex input dependencies using vine copulas

Emiliano Torre, Stefano Marelli, Paul Embrechts and Bruno Sudret
Probabilistic Engineering Mechanics 55 1 (2019)
DOI: 10.1016/j.probengmech.2018.08.001
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Dimension adaptive finite difference decomposition using multiple sparse grids for stochastic computation

Amit Kumar Rathi and Arunasis Chakraborty
Structural Safety 75 119 (2018)
DOI: 10.1016/j.strusafe.2018.06.004
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Optimization with constraints considering polymorphic uncertainties

Markus Mäck, Ismail Caylak, Philipp Edler, et al.
GAMM-Mitteilungen 42 (1) e201900005 (2019)
DOI: 10.1002/gamm.201900005
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Uncertainty quantification methodology for hyperbolic systems with application to blood flow in arteries

M. Petrella, S. Tokareva and E.F. Toro
Journal of Computational Physics 386 405 (2019)
DOI: 10.1016/j.jcp.2019.02.013
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Data-driven uncertainty quantification for Formula 1: Diffuser, wing tip and front wing variations

Richard Ahlfeld, Fabio Ciampoli, Marco Pietropaoli, Nick Pepper and Francesco Montomoli
Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 233 (6) 1495 (2019)
DOI: 10.1177/0954407019835315
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A generalized multi-resolution expansion for uncertainty propagation with application to cardiovascular modeling

D.E. Schiavazzi, A. Doostan, G. Iaccarino and A.L. Marsden
Computer Methods in Applied Mechanics and Engineering 314 196 (2017)
DOI: 10.1016/j.cma.2016.09.024
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Uncertainty quantification in LES of a turbulent bluff-body stabilized flame

Mohammad Khalil, Guilhem Lacaze, Joseph C. Oefelein and Habib N. Najm
Proceedings of the Combustion Institute 35 (2) 1147 (2015)
DOI: 10.1016/j.proci.2014.05.030
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A note on stochastic polynomial chaos expansions for uncertain volatility and Asian option pricing

Y.-T. Lin, Y.-T. Shih, C.-S. Chien and Q. Sheng
Applied Mathematics and Computation 393 125764 (2021)
DOI: 10.1016/j.amc.2020.125764
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Inverse uncertainty quantification of reactor simulations under the Bayesian framework using surrogate models constructed by polynomial chaos expansion

Xu Wu and Tomasz Kozlowski
Nuclear Engineering and Design 313 29 (2017)
DOI: 10.1016/j.nucengdes.2016.11.032
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On the convergence of the quasi-regression method: polynomial chaos and regularity

Je Guk Kim
Journal of Applied Probability 54 (2) 424 (2017)
DOI: 10.1017/jpr.2017.9
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Sparse Recovery via ℓq-Minimization for Polynomial Chaos Expansions

Ling Guo, Yongle Liu and Liang Yan
Numerical Mathematics: Theory, Methods and Applications 10 (4) 775 (2017)
DOI: 10.4208/nmtma.2017.0001
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Application of gPCRK Methods to Nonlinear Random Differential Equations with Piecewise Constant Argument

Chengjian Zhang and Wenjie Shi
East Asian Journal on Applied Mathematics 7 (2) 306 (2017)
DOI: 10.4208/eajam.150616.071216a
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Random field representations for stochastic elliptic boundary value problems and statistical inverse problems

A. NOUY and C. SOIZE
European Journal of Applied Mathematics 25 (3) 339 (2014)
DOI: 10.1017/S0956792514000072
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Compressed Principal Component Analysis of Non-Gaussian Vectors

Marc Mignolet and Christian Soize
SIAM/ASA Journal on Uncertainty Quantification 8 (4) 1261 (2020)
DOI: 10.1137/20M1322029
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Combining Polynomial Chaos Expansions and the Random Variable Transformation Technique to Approximate the Density Function of Stochastic Problems, Including Some Epidemiological Models

Julia Calatayud Gregori, Benito M. Chen-Charpentier, Juan Carlos Cortés López and Marc Jornet Sanz
Symmetry 11 (1) 43 (2019)
DOI: 10.3390/sym11010043
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Asymptotic expansion for some local volatility models arising in finance

Sergio Albeverio, Francesco Cordoni, Luca Di Persio and Gregorio Pellegrini
Decisions in Economics and Finance 42 (2) 527 (2019)
DOI: 10.1007/s10203-019-00247-w
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Phase driven study for stochastic linear multi-dofs dynamic response

E. Sarrouy
Mechanical Systems and Signal Processing 129 717 (2019)
DOI: 10.1016/j.ymssp.2019.04.042
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Handbook of Uncertainty Quantification

Christian Soize
Handbook of Uncertainty Quantification 1 (2015)
DOI: 10.1007/978-3-319-11259-6_30-1
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Handbook of Uncertainty Quantification

Bert Debusschere
Handbook of Uncertainty Quantification 1 (2015)
DOI: 10.1007/978-3-319-11259-6_19-1
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A hyperbolicity-preserving discontinuous stochastic Galerkin scheme for uncertain hyperbolic systems of equations

Jakob Dürrwächter, Thomas Kuhn, Fabian Meyer, Louisa Schlachter and Florian Schneider
Journal of Computational and Applied Mathematics 370 112602 (2020)
DOI: 10.1016/j.cam.2019.112602
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Numerical approximation of poroelasticity with random coefficients using Polynomial Chaos and Hybrid High-Order methods

Michele Botti, Daniele A. Di Pietro, Olivier Le Maître and Pierre Sochala
Computer Methods in Applied Mechanics and Engineering 361 112736 (2020)
DOI: 10.1016/j.cma.2019.112736
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A two-stage surrogate model for Neo-Hookean problems based on adaptive proper orthogonal decomposition and hierarchical tensor approximation

Steffen Kastian, Dieter Moser, Lars Grasedyck and Stefanie Reese
Computer Methods in Applied Mechanics and Engineering 372 113368 (2020)
DOI: 10.1016/j.cma.2020.113368
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Sensitivity Analysis of Burgers' Equation with Shocks

Qin Li, Jian-Guo Liu and Ruiwen Shu
SIAM/ASA Journal on Uncertainty Quantification 8 (4) 1493 (2020)
DOI: 10.1137/18M1211763
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A hybrid stochastic domain decomposition method for partial differential equations with localised possibly rough random data

Robert Gruhlke, Martin Eigel, Dietmar Hömberg, Martin Drieschner and Yuri Petryna
PAMM 18 (1) e201800434 (2018)
DOI: 10.1002/pamm.201800434
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Reservoir Computing Universality With Stochastic Inputs

Lukas Gonon and Juan-Pablo Ortega
IEEE Transactions on Neural Networks and Learning Systems 31 (1) 100 (2020)
DOI: 10.1109/TNNLS.2019.2899649
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A Spline Chaos Expansion

Sharif Rahman
SIAM/ASA Journal on Uncertainty Quantification 8 (1) 27 (2020)
DOI: 10.1137/19M1239702
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Global sensitivity analysis with a hierarchical sparse metamodeling method

Wei Zhao and Lingze Bu
Mechanical Systems and Signal Processing 115 769 (2019)
DOI: 10.1016/j.ymssp.2018.06.044
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Sparse polynomial surrogates for non-intrusive, high-dimensional uncertainty quantification of aeroelastic computations

Éric Savin and Jean-Luc Hantrais-Gervois
Probabilistic Engineering Mechanics 59 103027 (2020)
DOI: 10.1016/j.probengmech.2020.103027
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Random Fields for Spatial Data Modeling

Dionissios T. Hristopulos
Advances in Geographic Information Science, Random Fields for Spatial Data Modeling 689 (2020)
DOI: 10.1007/978-94-024-1918-4_16
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On spectral methods for variance based sensitivity analysis

Alen Alexanderian
Probability Surveys 10 (none) (2013)
DOI: 10.1214/13-PS219
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Computing the density function of complex models with randomness by using polynomial expansions and the RVT technique. Application to the SIR epidemic model

Julia Calatayud, Juan Carlos Cortés and Marc Jornet
Chaos, Solitons & Fractals 133 109639 (2020)
DOI: 10.1016/j.chaos.2020.109639
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Computing Invariant Sets of Random Differential Equations Using Polynomial Chaos

Maxime Breden and Christian Kuehn
SIAM Journal on Applied Dynamical Systems 19 (1) 577 (2020)
DOI: 10.1137/18M1235818
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Beyond the hypothesis of boundedness for the random coefficient of Airy, Hermite and Laguerre differential equations with uncertainties

Julia Calatayud Gregori, Juan-Carlos Cortés and Marc Jornet Sanz
Stochastic Analysis and Applications 38 (5) 875 (2020)
DOI: 10.1080/07362994.2020.1733017
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Improving the Approximation of the First- and Second-Order Statistics of the Response Stochastic Process to the Random Legendre Differential Equation

J. Calatayud, J.-C. Cortés and M. Jornet
Mediterranean Journal of Mathematics 16 (3) (2019)
DOI: 10.1007/s00009-019-1338-6
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Uncertainty quantification in a hydrogen production system based on the solar hybrid sulfur process

M. Venturin, L. Turchetti and R. Liberatore
International Journal of Hydrogen Energy 45 (29) 14679 (2020)
DOI: 10.1016/j.ijhydene.2020.03.200
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Current Trends in Dynamical Systems in Biology and Natural Sciences

Francesco Florian and Rossana Vermiglio
SEMA SIMAI Springer Series, Current Trends in Dynamical Systems in Biology and Natural Sciences 21 205 (2020)
DOI: 10.1007/978-3-030-41120-6_11
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Reliability-Based Optimization for Energy Refurbishment of a Social Housing Building

Marco Manzan, Giorgio Lupato, Amedeo Pezzi, Paolo Rosato and Alberto Clarich
Energies 13 (9) 2310 (2020)
DOI: 10.3390/en13092310
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On the Construction of Uncertain Time Series Surrogates Using Polynomial Chaos and Gaussian Processes

Pierre Sochala and Mohamed Iskandarani
Mathematical Geosciences 52 (2) 285 (2020)
DOI: 10.1007/s11004-019-09806-8
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Spectral convergence of the generalized Polynomial Chaos reduced model obtained from the uncertain linear Boltzmann equation

Gaël Poëtte
Mathematics and Computers in Simulation 177 24 (2020)
DOI: 10.1016/j.matcom.2020.04.009
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Robust topology optimization for heat conduction with polynomial chaos expansion

André Jacomel Torii, Diogo Pereira da Silva Santos and Eduardo Morais de Medeiros
Journal of the Brazilian Society of Mechanical Sciences and Engineering 42 (6) (2020)
DOI: 10.1007/s40430-020-02367-6
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Modeling of Allee effect in biofilm formation via the stochastic bistable Allen–Cahn partial differential equation

Marc Jornet
Stochastic Analysis and Applications 39 (1) 22 (2021)
DOI: 10.1080/07362994.2020.1777163
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A posteriori error estimation and adaptivity in stochastic Galerkin FEM for parametric elliptic PDEs: Beyond the affine case

Alex Bespalov and Feng Xu
Computers & Mathematics with Applications 80 (5) 1084 (2020)
DOI: 10.1016/j.camwa.2020.05.023
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Uncertainty Propagation Using Polynomial Chaos Expansions for Extreme Sea Level Hazard Assessment: The Case of the Eastern Adriatic Meteotsunamis

Cléa Denamiel, Xun Huan, Jadranka Šepić and Ivica Vilibić
Journal of Physical Oceanography 50 (4) 1005 (2020)
DOI: 10.1175/JPO-D-19-0147.1
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Non-intrusive framework of reduced-order modeling based on proper orthogonal decomposition and polynomial chaos expansion

Xiang Sun, Xiaomin Pan and Jung-Il Choi
Journal of Computational and Applied Mathematics 390 113372 (2021)
DOI: 10.1016/j.cam.2020.113372
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Extending bluff-and-fix estimates for polynomial chaos expansions

Laura Lyman and Gianluca Iaccarino
Journal of Computational Science 50 101287 (2021)
DOI: 10.1016/j.jocs.2020.101287
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Wick–Malliavin approximation to nonlinear stochastic partial differential equations: analysis and simulations

D. Venturi, X. Wan, R. Mikulevicius, B. L. Rozovskii and G. E. Karniadakis
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469 (2158) 20130001 (2013)
DOI: 10.1098/rspa.2013.0001
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Uncertainty Quantification for Fat-Tailed Probability Distributions in Aircraft Engine Simulations

R. Ahlfeld, F. Montomoli, E. Scalas and S. Shahpar
Journal of Propulsion and Power 33 (4) 881 (2017)
DOI: 10.2514/1.B36278
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Convergence Analysis and Adaptive Order Selection for the Polynomial Chaos Approach to Direct Optimal Control under Uncertainties

Lilli Frison and Christian Kirches
SIAM Journal on Control and Optimization 59 (1) 509 (2021)
DOI: 10.1137/17M1133038
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Solution of the 3D density-driven groundwater flow problem with uncertain porosity and permeability

Alexander Litvinenko, Dmitry Logashenko, Raul Tempone, Gabriel Wittum and David Keyes
GEM - International Journal on Geomathematics 11 (1) (2020)
DOI: 10.1007/s13137-020-0147-1
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The numerical approximation of nonlinear functionals and functional differential equations

Daniele Venturi
Physics Reports 732 1 (2018)
DOI: 10.1016/j.physrep.2017.12.003
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A polynomial chaos expansion in dependent random variables

Sharif Rahman
Journal of Mathematical Analysis and Applications 464 (1) 749 (2018)
DOI: 10.1016/j.jmaa.2018.04.032
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Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks

Sharmila Karumuri, Rohit Tripathy, Ilias Bilionis and Jitesh Panchal
Journal of Computational Physics 404 109120 (2020)
DOI: 10.1016/j.jcp.2019.109120
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Uncertainty quantification for the random viscous Burgers’ partial differential equation by using the differential transform method

Marc Jornet
Nonlinear Analysis 209 112340 (2021)
DOI: 10.1016/j.na.2021.112340
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Development of hybrid dimension adaptive sparse HDMR for stochastic finite element analysis of composite plate

Amit Kumar Rathi and Arunasis Chakraborty
Composite Structures 255 112915 (2021)
DOI: 10.1016/j.compstruct.2020.112915
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Parseval inequalities and lower bounds for variance-based sensitivity indices

Olivier Roustant, Fabrice Gamboa and Bertrand Iooss
Electronic Journal of Statistics 14 (1) (2020)
DOI: 10.1214/19-EJS1673
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Non-intrusive polynomial chaos methods for uncertainty quantification in wave problems at high frequencies

Nabil El Mocayd, M Shadi Mohamed and Mohammed Seaid
Journal of Computational Science 101344 (2021)
DOI: 10.1016/j.jocs.2021.101344
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Data-driven polynomial chaos expansion for machine learning regression

Emiliano Torre, Stefano Marelli, Paul Embrechts and Bruno Sudret
Journal of Computational Physics 388 601 (2019)
DOI: 10.1016/j.jcp.2019.03.039
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Hyperbolic stochastic Galerkin formulation for the p-system

Stephan Gerster, Michael Herty and Aleksey Sikstel
Journal of Computational Physics 395 186 (2019)
DOI: 10.1016/j.jcp.2019.05.049
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Multi-fidelity Gaussian process regression for prediction of random fields

L. Parussini, D. Venturi, P. Perdikaris and G.E. Karniadakis
Journal of Computational Physics 336 36 (2017)
DOI: 10.1016/j.jcp.2017.01.047
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Uncertainty quantification of simulated biomechanical stimuli in coronary artery bypass grafts

Justin S. Tran, Daniele E. Schiavazzi, Andrew M. Kahn and Alison L. Marsden
Computer Methods in Applied Mechanics and Engineering 345 402 (2019)
DOI: 10.1016/j.cma.2018.10.024
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Polynomial chaos expansions for dependent random variables

John D. Jakeman, Fabian Franzelin, Akil Narayan, Michael Eldred and Dirk Plfüger
Computer Methods in Applied Mechanics and Engineering 351 643 (2019)
DOI: 10.1016/j.cma.2019.03.049
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Hyperbolicity-Preserving and Well-Balanced Stochastic Galerkin Method for Shallow Water Equations

Dihan Dai, Yekaterina Epshteyn and Akil Narayan
SIAM Journal on Scientific Computing 43 (2) A929 (2021)
DOI: 10.1137/20M1360736
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