EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues ESAIM: M2AN, 46 2 (2012) 317-339 Article references

Articles citing this article

The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).

Cited article:

This article has been cited by the following article(s):

Encyclopedia of Computational Mechanics Second Edition

Hermann G. Matthies
Encyclopedia of Computational Mechanics Second Edition 1 (2018)
DOI: 10.1002/9781119176817.ecm2071
See this article

Generalized polynomial chaos for nonlinear random delay differential equations

Wenjie Shi and Chengjian Zhang
Applied Numerical Mathematics 115 16 (2017)
DOI: 10.1016/j.apnum.2016.12.004
See this article

Inverse modeling of geochemical and mechanical compaction in sedimentary basins through Polynomial Chaos Expansion

G. Porta, L. Tamellini, V. Lever and M. Riva
Water Resources Research 50 (12) 9414 (2014)
DOI: 10.1002/2014WR015838
See this article

Numerical Procedures for Random Differential Equations

Mohamed Ben Said, Lahcen Azrar and Driss Sarsri
Journal of Applied Mathematics 2018 1 (2018)
DOI: 10.1155/2018/7403745
See this article

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 e2776 (2020)
DOI: 10.1002/jnm.2776
See this article

Measure transformation and efficient quadrature in reduced-dimensional stochastic modeling of coupled problems

M. Arnst, R. Ghanem, E. Phipps and J. Red-Horse
International Journal for Numerical Methods in Engineering 92 (12) 1044 (2012)
DOI: 10.1002/nme.4368
See this article

A second order SAP algorithm for risk and reliability based design optimization

A.J. Torii, R.H. Lopez and L.F.F. Miguel
Reliability Engineering & System Safety 190 106499 (2019)
DOI: 10.1016/j.ress.2019.106499
See this article

Model order reduction for random nonlinear dynamical systems and low-dimensional representations for their quantities of interest

Roland Pulch
Mathematics and Computers in Simulation 166 76 (2019)
DOI: 10.1016/j.matcom.2019.01.016
See this article

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
See this article

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
See this article

Uncertainty Quantification

Christian Soize
Interdisciplinary Applied Mathematics, Uncertainty Quantification 47 245 (2017)
DOI: 10.1007/978-3-319-54339-0_10
See this article

Uncertainty Quantification

Christian Soize
Interdisciplinary Applied Mathematics, Uncertainty Quantification 47 133 (2017)
DOI: 10.1007/978-3-319-54339-0_6
See this article

Adaptive stochastic Galerkin FEM for lognormal coefficients in hierarchical tensor representations

Martin Eigel, Manuel Marschall, Max Pfeffer and Reinhold Schneider
Numerische Mathematik 145 (3) 655 (2020)
DOI: 10.1007/s00211-020-01123-1
See this article

Stochastic collocation and stochastic Galerkin methods for linear differential algebraic equations

Roland Pulch
Journal of Computational and Applied Mathematics 262 281 (2014)
DOI: 10.1016/j.cam.2013.10.046
See this article

Pitfalls in the frequency response represented onto Polynomial Chaos for random SDOF mechanical systems

E. Pagnacco, E. Sarrouy, R. Sampaio and E. Souza de Cursi
Applied Mathematical Modelling 52 626 (2017)
DOI: 10.1016/j.apm.2017.08.004
See this article

Constructing adaptive generalized polynomial chaos method to measure the uncertainty in continuous models: A computational approach

B.-M. Chen-Charpentier, J.-C. Cortés, J.-A. Licea, et al.
Mathematics and Computers in Simulation 109 113 (2015)
DOI: 10.1016/j.matcom.2014.09.002
See this article

Optimal Bayesian experimental design for subsurface flow problems

Alexadner Tarakanov and Ahmed H. Elsheikh
Computer Methods in Applied Mechanics and Engineering 370 113208 (2020)
DOI: 10.1016/j.cma.2020.113208
See this article

Model order reduction and low-dimensional representations for random linear dynamical systems

Roland Pulch
Mathematics and Computers in Simulation 144 1 (2018)
DOI: 10.1016/j.matcom.2017.05.007
See this article

Sparse Grids and Applications - Munich 2012

Oliver G. Ernst and Björn Sprungk
Lecture Notes in Computational Science and Engineering, Sparse Grids and Applications - Munich 2012 97 29 (2014)
DOI: 10.1007/978-3-319-04537-5_2
See this article

Equations Involving Malliavin Calculus Operators

Tijana Levajković and Hermann Mena
SpringerBriefs in Mathematics, Equations Involving Malliavin Calculus Operators 75 (2017)
DOI: 10.1007/978-3-319-65678-6_3
See this article

Extraction of Quantifiable Information from Complex Systems

Oliver G. Ernst, Björn Sprungk and Hans-Jörg Starkloff
Lecture Notes in Computational Science and Engineering, Extraction of Quantifiable Information from Complex Systems 102 133 (2014)
DOI: 10.1007/978-3-319-08159-5_7
See this article

Theory and Practice of Risk Assessment

Teresa A. Oliveira, Conceição Leal and Amílcar Oliveira
Springer Proceedings in Mathematics & Statistics, Theory and Practice of Risk Assessment 136 385 (2015)
DOI: 10.1007/978-3-319-18029-8_29
See this article

Coupled Multiscale Simulation and Optimization in Nanoelectronics

Gabriela Ciuprina, Jorge Fernández Villena, Daniel Ioan, et al.
Mathematics in Industry, Coupled Multiscale Simulation and Optimization in Nanoelectronics 21 267 (2015)
DOI: 10.1007/978-3-662-46672-8_5
See this article

Polynomial Chaos Methods for Hyperbolic Partial Differential Equations

Mass Per Pettersson, Jan Nordström and Gianluca Iaccarino
Mathematical Engineering, Polynomial Chaos Methods for Hyperbolic Partial Differential Equations 11 (2015)
DOI: 10.1007/978-3-319-10714-1_2
See this article

Emerging Applications of Control and Systems Theory

Joel A. Paulson, Eranda Harinath, Lucas C. Foguth and Richard D. Braatz
Lecture Notes in Control and Information Sciences - Proceedings, Emerging Applications of Control and Systems Theory 63 (2018)
DOI: 10.1007/978-3-319-67068-3_5
See this article

Polynomial Chaos Expansion of a Multimodal Random Vector

C. Soize
SIAM/ASA Journal on Uncertainty Quantification 3 (1) 34 (2015)
DOI: 10.1137/140968495
See this article

Introduction to Uncertainty Quantification

T. J. Sullivan
Texts in Applied Mathematics, Introduction to Uncertainty Quantification 63 133 (2015)
DOI: 10.1007/978-3-319-23395-6_8
See this article

Stochastic Collocation Methods on Unstructured Grids in High Dimensions via Interpolation

Akil Narayan and Dongbin Xiu
SIAM Journal on Scientific Computing 34 (3) A1729 (2012)
DOI: 10.1137/110854059
See this article

Influence of Physical and Geometrical Uncertainties in the Parametric Instability Load of an Axially Excited Cylindrical Shell

Frederico Martins Alves da Silva, Augusta Finotti Brazão and Paulo Batista Gonçalves
Mathematical Problems in Engineering 2015 1 (2015)
DOI: 10.1155/2015/758959
See this article

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
See this article

Efficient Uncertainty Quantification in Stochastic Economic Dispatch

Cosmin Safta, Richard L.-Y. Chen, Habib N. Najm, Ali Pinar and Jean-Paul Watson
IEEE Transactions on Power Systems 32 (4) 2535 (2017)
DOI: 10.1109/TPWRS.2016.2615334
See this article

Analysis of the Ensemble and Polynomial Chaos Kalman Filters in Bayesian Inverse Problems

Oliver G. Ernst, Björn Sprungk and Hans-Jörg Starkloff
SIAM/ASA Journal on Uncertainty Quantification 3 (1) 823 (2015)
DOI: 10.1137/140981319
See this article

Quantifying Sampling Noise and Parametric Uncertainty in Atomistic-to-Continuum Simulations Using Surrogate Models

Maher Salloum, Khachik Sargsyan, Reese Jones, Habib N. Najm and Bert Debusschere
Multiscale Modeling & Simulation 13 (3) 953 (2015)
DOI: 10.1137/140989601
See this article

Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion

S. Oladyshkin and W. Nowak
Reliability Engineering & System Safety 106 179 (2012)
DOI: 10.1016/j.ress.2012.05.002
See this article

Handbook of Uncertainty Quantification

Khachik Sargsyan
Handbook of Uncertainty Quantification 1 (2015)
DOI: 10.1007/978-3-319-11259-6_22-1
See this article

Variational Theory and Computations in Stochastic Plasticity

Bojana V. Rosić and Hermann G. Matthies
Archives of Computational Methods in Engineering 22 (3) 457 (2015)
DOI: 10.1007/s11831-014-9116-x
See this article

Dynamical Polynomial Chaos Expansions and Long Time Evolution of Differential Equations with Random Forcing

H. Cagan Ozen and Guillaume Bal
SIAM/ASA Journal on Uncertainty Quantification 4 (1) 609 (2016)
DOI: 10.1137/15M1019167
See this article

Adaptive stochastic Galerkin FEM

Martin Eigel, Claude Jeffrey Gittelson, Christoph Schwab and Elmar Zander
Computer Methods in Applied Mechanics and Engineering 270 247 (2014)
DOI: 10.1016/j.cma.2013.11.015
See this article

Subspace inverse power method and polynomial chaos representation for the modal frequency responses of random mechanical systems

E. Pagnacco, E. Souza de Cursi and R. Sampaio
Computational Mechanics 58 (1) 129 (2016)
DOI: 10.1007/s00466-016-1285-z
See this article

Low-Rank Solution of Unsteady Diffusion Equations with Stochastic Coefficients

Peter Benner, Akwum Onwunta and Martin Stoll
SIAM/ASA Journal on Uncertainty Quantification 3 (1) 622 (2015)
DOI: 10.1137/130937251
See this article

Adaptive wavelet methods for the stochastic Poisson equation

Petru A. Cioica, Stephan Dahlke, Nicolas Döhring, et al.
BIT Numerical Mathematics 52 (3) 589 (2012)
DOI: 10.1007/s10543-011-0368-7
See this article

Error analysis of generalized polynomial chaos for nonlinear random ordinary differential equations

Wenjie Shi and Chengjian Zhang
Applied Numerical Mathematics 62 (12) 1954 (2012)
DOI: 10.1016/j.apnum.2012.08.007
See this article

An accuracy comparison of polynomial chaos type methods for the propagation of uncertainties

Florian Augustin, Albert Gilg, Meinhard Paffrath, et al.
Journal of Mathematics in Industry 3 (1) 2 (2013)
DOI: 10.1186/2190-5983-3-2
See this article

Stochastic Galerkin techniques for random ordinary differential equations

F. Augustin and P. Rentrop
Numerische Mathematik 122 (3) 399 (2012)
DOI: 10.1007/s00211-012-0466-8
See this article

Emulation to simulate low-resolution atmospheric data

Vishwas Rao, Rick Archibald and Katherine J. Evans
International Journal of Computer Mathematics 91 (4) 770 (2014)
DOI: 10.1080/00207160.2013.852663
See this article

Ambrosio-Tortorelli Segmentation of Stochastic Images: Model Extensions, Theoretical Investigations and Numerical Methods

Torben Pätz, Robert M. Kirby and Tobias Preusser
International Journal of Computer Vision 103 (2) 190 (2013)
DOI: 10.1007/s11263-012-0578-8
See this article

Analysis of Discrete $$L^2$$ L 2 Projection on Polynomial Spaces with Random Evaluations

G. Migliorati, F. Nobile, E. von Schwerin and R. Tempone
Foundations of Computational Mathematics 14 (3) 419 (2014)
DOI: 10.1007/s10208-013-9186-4
See this article

Enforcing positivity in intrusive PC-UQ methods for reactive ODE systems

Habib N. Najm and Mauro Valorani
Journal of Computational Physics 270 544 (2014)
DOI: 10.1016/j.jcp.2014.03.061
See this article

Long-time uncertainty propagation using generalized polynomial chaos and flow map composition

Dirk M. Luchtenburg, Steven L. Brunton and Clarence W. Rowley
Journal of Computational Physics 274 783 (2014)
DOI: 10.1016/j.jcp.2014.06.029
See this article

Uncertainty quantification of reaction mechanisms accounting for correlations introduced by rate rules and fitted Arrhenius parameters

Jens Prager, Habib N. Najm, Khachik Sargsyan, Cosmin Safta and William J. Pitz
Combustion and Flame 160 (9) 1583 (2013)
DOI: 10.1016/j.combustflame.2013.01.008
See this article

Stochastic Collocation Methods via $\ell_1$ Minimization Using Randomized Quadratures

Ling Guo, Akil Narayan, Tao Zhou and Yuhang Chen
SIAM Journal on Scientific Computing 39 (1) A333 (2017)
DOI: 10.1137/16M1059680
See this article

Fundamental equations with higher order Malliavin operators

Tijana Levajković, Stevan Pilipović and Dora Seleši
Stochastics 88 (1) 106 (2016)
DOI: 10.1080/17442508.2015.1036434
See this article

Global sensitivity analysis of the impact of impurities on CO2 pipeline failure

S. Brown, J. Beck, H. Mahgerefteh and E.S. Fraga
Reliability Engineering & System Safety 115 43 (2013)
DOI: 10.1016/j.ress.2013.02.006
See this article

Computational uncertainty quantification for random non-autonomous second order linear differential equations via adapted gPC: a comparative case study with random Fröbenius method and Monte Carlo simulation

Julia Calatayud, Juan Carlos Cortés and Marc Jornet
Open Mathematics 16 (1) 1651 (2018)
DOI: 10.1515/math-2018-0134
See this article

Low-rank solvers for unsteady Stokes–Brinkman optimal control problem with random data

Peter Benner, Sergey Dolgov, Akwum Onwunta and Martin Stoll
Computer Methods in Applied Mechanics and Engineering 304 26 (2016)
DOI: 10.1016/j.cma.2016.02.004
See this article

Improving adaptive generalized polynomial chaos method to solve nonlinear random differential equations by the random variable transformation technique

J.-C. Cortés, J.-V. Romero, M.-D. Roselló and R.-J. Villanueva
Communications in Nonlinear Science and Numerical Simulation 50 1 (2017)
DOI: 10.1016/j.cnsns.2017.02.011
See this article

Wiener–Poisson chaos expansion and numerical solutions of the Heath–Jarrow–Morton interest rate model

Evangelia A. Kalpinelli and Nikolaos E. Frangos
Stochastics and Partial Differential Equations: Analysis and Computations 4 (2) 361 (2016)
DOI: 10.1007/s40072-015-0066-6
See this article

Probability of failure sensitivity analysis using polynomial expansion

André Jacomel Torii, Rafael Holdorf Lopez and Leandro Fleck Fadel Miguel
Probabilistic Engineering Mechanics 48 76 (2017)
DOI: 10.1016/j.probengmech.2017.06.001
See this article

Uncertainty quantification in LES of channel flow

Cosmin Safta, Myra Blaylock, Jeremy Templeton, et al.
International Journal for Numerical Methods in Fluids 83 (4) 376 (2017)
DOI: 10.1002/fld.4272
See this article

Arbitrary Polynomial Chaos for Uncertainty Propagation of Correlated Random Variables in Dynamic Systems

Joel A. Paulson, Edward A. Buehler and Ali Mesbah
IFAC-PapersOnLine 50 (1) 3548 (2017)
DOI: 10.1016/j.ifacol.2017.08.954
See this article

Some greedy algorithms for sparse polynomial chaos expansions

Ricardo Baptista, Valentin Stolbunov and Prasanth B. Nair
Journal of Computational Physics 387 303 (2019)
DOI: 10.1016/j.jcp.2019.01.035
See this article

Adaptive Smolyak Pseudospectral Approximations

Patrick R. Conrad and Youssef M. Marzouk
SIAM Journal on Scientific Computing 35 (6) A2643 (2013)
DOI: 10.1137/120890715
See this article

Stability Preservation in Stochastic Galerkin Projections of Dynamical Systems

Roland Pulch and Florian Augustin
SIAM/ASA Journal on Uncertainty Quantification 7 (2) 634 (2019)
DOI: 10.1137/17M1142223
See this article

High order approximation of probabilistic shock profiles in hyperbolic conservation laws with uncertain initial data

Christoph Schwab and Svetlana Tokareva
ESAIM: Mathematical Modelling and Numerical Analysis 47 (3) 807 (2013)
DOI: 10.1051/m2an/2012060
See this article

Global Sensitivity Analysis and Estimation of Model Error, Toward Uncertainty Quantification in Scramjet Computations

Xun Huan, Cosmin Safta, Khachik Sargsyan, et al.
AIAA Journal 56 (3) 1170 (2018)
DOI: 10.2514/1.J056278
See this article

On stability and monotonicity requirements of finite difference approximations of stochastic conservation laws with random viscosity

Per Pettersson, Alireza Doostan and Jan Nordström
Computer Methods in Applied Mechanics and Engineering 258 134 (2013)
DOI: 10.1016/j.cma.2013.02.009
See this article

Modified SFEM for computational homogenization of heterogeneous materials with microstructural geometric uncertainties

Dmytro Pivovarov and Paul Steinmann
Computational Mechanics 57 (1) 123 (2016)
DOI: 10.1007/s00466-015-1224-4
See this article

Probabilistic Density Function Method for Stochastic ODEs of Power Systems with Uncertain Power Input

P. Wang, D. A. Barajas-Solano, E. Constantinescu, et al.
SIAM/ASA Journal on Uncertainty Quantification 3 (1) 873 (2015)
DOI: 10.1137/130940050
See this article

Progress in Industrial Mathematics at ECMI 2016

Alexander Vibe and Nicole Marheineke
Mathematics in Industry, Progress in Industrial Mathematics at ECMI 2016 26 761 (2017)
DOI: 10.1007/978-3-319-63082-3_112
See this article

Preconditioned Bayesian Regression for Stochastic Chemical Kinetics

Alen Alexanderian, Francesco Rizzi, Muruhan Rathinam, Olivier P. Le Maître and Omar M. Knio
Journal of Scientific Computing 58 (3) 592 (2014)
DOI: 10.1007/s10915-013-9745-5
See this article

On the convergence of the stochastic Galerkin method for random elliptic partial differential equations

Antje Mugler and Hans-Jörg Starkloff
ESAIM: Mathematical Modelling and Numerical Analysis 47 (5) 1237 (2013)
DOI: 10.1051/m2an/2013066
See this article

A data driven polynomial chaos based approach for stochastic analysis of CFRP laminated composite plates

P. Sasikumar, A. Venketeswaran, R. Suresh and Sayan Gupta
Composite Structures 125 212 (2015)
DOI: 10.1016/j.compstruct.2015.02.010
See this article

Shape and topology optimization of a permanent-magnet machine under uncertainties

Piotr Putek, Roland Pulch, Andreas Bartel, et al.
Journal of Mathematics in Industry 6 (1) (2016)
DOI: 10.1186/s13362-016-0032-6
See this article

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
See this article

Probabilistic parameter estimation in a 2-step chemical kinetics model for n-dodecane jet autoignition

Layal Hakim, Guilhem Lacaze, Mohammad Khalil, et al.
Combustion Theory and Modelling 22 (3) 446 (2018)
DOI: 10.1080/13647830.2017.1403653
See this article

Predicting reinforcing bar development length using polynomial chaos expansions

Zaher Mundher Yaseen, Behrooz Keshtegar, Hyeon-Jong Hwang and Moncef L. Nehdi
Engineering Structures 195 524 (2019)
DOI: 10.1016/j.engstruct.2019.06.012
See this article

Convergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficients

Joakim Beck, Fabio Nobile, Lorenzo Tamellini and Raúl Tempone
Computers & Mathematics with Applications 67 (4) 732 (2014)
DOI: 10.1016/j.camwa.2013.03.004
See this article

Mathematical Properties of Polynomial Dimensional Decomposition

Sharif Rahman
SIAM/ASA Journal on Uncertainty Quantification 6 (2) 816 (2018)
DOI: 10.1137/16M1109382
See this article

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
See this article

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
See this article

N-TERM WIENER CHAOS APPROXIMATION RATES FOR ELLIPTIC PDEs WITH LOGNORMAL GAUSSIAN RANDOM INPUTS

VIET HA HOANG and CHRISTOPH SCHWAB
Mathematical Models and Methods in Applied Sciences 24 (04) 797 (2014)
DOI: 10.1142/S0218202513500681
See this article

ON THE OPTIMAL POLYNOMIAL APPROXIMATION OF STOCHASTIC PDES BY GALERKIN AND COLLOCATION METHODS

JOAKIM BECK, RAUL TEMPONE, FABIO NOBILE and LORENZO TAMELLINI
Mathematical Models and Methods in Applied Sciences 22 (09) 1250023 (2012)
DOI: 10.1142/S0218202512500236
See this article

Uncertainty Quantification in Computational Fluid Dynamics and Aircraft Engines

M. Carnevale and R. Ahlfeld
Uncertainty Quantification in Computational Fluid Dynamics and Aircraft Engines 67 (2019)
DOI: 10.1007/978-3-319-92943-9_3
See this article

Compressive Sensing with Cross-Validation and Stop-Sampling for Sparse Polynomial Chaos Expansions

Xun Huan, Cosmin Safta, Khachik Sargsyan, et al.
SIAM/ASA Journal on Uncertainty Quantification 6 (2) 907 (2018)
DOI: 10.1137/17M1141096
See this article

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
See this article

On the Construction of Stochastic Fields with Prescribed Regularity by Wavelet Expansions

Stephan Dahlke, Nicolas Döhring and Stefan Kinzel
Vietnam Journal of Mathematics 46 (3) 557 (2018)
DOI: 10.1007/s10013-017-0258-7
See this article

A constant phase approach for the frequency response of stochastic linear oscillators

Emmanuelle Sarrouy, Emmanuel Pagnacco and Eduardo Souza de Cursi
Mechanics & Industry 17 (2) 206 (2016)
DOI: 10.1051/meca/2015057
See this article

Multi-element least square HDMR methods and their applications for stochastic multiscale model reduction

Lijian Jiang and Xinping Li
Journal of Computational Physics 294 439 (2015)
DOI: 10.1016/j.jcp.2015.03.066
See this article

Parametrization of Random Vectors in Polynomial Chaos Expansions via Optimal Transportation

Faidra Stavropoulou and Johannes Müller
SIAM Journal on Scientific Computing 37 (6) A2535 (2015)
DOI: 10.1137/130949063
See this article

Algorithms for Propagating Uncertainty Across Heterogeneous Domains

H. Cho, X. Yang, D. Venturi and G. E. Karniadakis
SIAM Journal on Scientific Computing 37 (6) A3030 (2015)
DOI: 10.1137/140992060
See this article

Uncertainty quantification in virtual surgery hemodynamics predictions for single ventricle palliation

D. E. Schiavazzi, G. Arbia, C. Baker, et al.
International Journal for Numerical Methods in Biomedical Engineering 32 (3) e02737 (2016)
DOI: 10.1002/cnm.2737
See this article

Probabilistic inference of reaction rate parameters from summary statistics

Mohammad Khalil and Habib N. Najm
Combustion Theory and Modelling 22 (4) 635 (2018)
DOI: 10.1080/13647830.2017.1370557
See this article

Polynomial Chaos Expansion Approach to Interest Rate Models

Luca Di Persio, Gregorio Pellegrini and Michele Bonollo
Journal of Probability and Statistics 2015 1 (2015)
DOI: 10.1155/2015/369053
See this article

SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

R. Ahlfeld, B. Belkouchi and F. Montomoli
Journal of Computational Physics 320 1 (2016)
DOI: 10.1016/j.jcp.2016.05.014
See this article

Operator differential-algebraic equations with noise arising in fluid dynamics

Robert Altmann, Tijana Levajković and Hermann Mena
Monatshefte für Mathematik 182 (4) 741 (2017)
DOI: 10.1007/s00605-016-0931-z
See this article

Polynomial chaos representation of databases on manifolds

C. Soize and R. Ghanem
Journal of Computational Physics 335 201 (2017)
DOI: 10.1016/j.jcp.2017.01.031
See this article

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
See this article

A dynamical polynomial chaos approach for long-time evolution of SPDEs

H. Cagan Ozen and Guillaume Bal
Journal of Computational Physics 343 300 (2017)
DOI: 10.1016/j.jcp.2017.04.054
See this article

On stochastic FEM based computational homogenization of magneto-active heterogeneous materials with random microstructure

Dmytro Pivovarov and Paul Steinmann
Computational Mechanics 58 (6) 981 (2016)
DOI: 10.1007/s00466-016-1329-4
See this article

Sparse Adaptive Tensor Galerkin Approximations of Stochastic PDE-Constrained Control Problems

Angela Kunoth and Christoph Schwab
SIAM/ASA Journal on Uncertainty Quantification 4 (1) 1034 (2016)
DOI: 10.1137/15M1041390
See this article

Efficient Iterative Solvers for Stochastic Galerkin Discretizations of Log-Transformed Random Diffusion Problems

Elisabeth Ullmann, Howard C. Elman and Oliver G. Ernst
SIAM Journal on Scientific Computing 34 (2) A659 (2012)
DOI: 10.1137/110836675
See this article

Constructing Nested Nodal Sets for Multivariate Polynomial Interpolation

Akil Narayan and Dongbin Xiu
SIAM Journal on Scientific Computing 35 (5) A2293 (2013)
DOI: 10.1137/12089613X
See this article

Local Polynomial Chaos Expansion for Linear Differential Equations with High Dimensional Random Inputs

Yi Chen, John Jakeman, Claude Gittelson and Dongbin Xiu
SIAM Journal on Scientific Computing 37 (1) A79 (2015)
DOI: 10.1137/140970100
See this article

Subsampled Gauss Quadrature Nodes for Estimating Polynomial Chaos Expansions

Gary Tang and Gianluca Iaccarino
SIAM/ASA Journal on Uncertainty Quantification 2 (1) 423 (2014)
DOI: 10.1137/130913511
See this article

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

G. Migliorati, F. Nobile, E. von Schwerin and R. Tempone
SIAM Journal on Scientific Computing 35 (3) A1440 (2013)
DOI: 10.1137/120897109
See this article

Uncertainty Management for Robust Industrial Design in Aeronautics

Chris Lacor and Éric Savin
Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Uncertainty Management for Robust Industrial Design in Aeronautics 140 687 (2019)
DOI: 10.1007/978-3-319-77767-2_42
See this article

The polynomial chaos approach for reachable set propagation with application to chance-constrained nonlinear optimal control under parametric uncertainties

Lilli Bergner and Christian Kirches
Optimal Control Applications and Methods 39 (2) 471 (2018)
DOI: 10.1002/oca.2329
See this article

Emulation of Numerical Models With Over-Specified Basis Functions

Avishek Chakraborty, Derek Bingham, Soma S. Dhavala, et al.
Technometrics 59 (2) 153 (2017)
DOI: 10.1080/00401706.2016.1164078
See this article

Wiener–Hermite polynomial expansion for multivariate Gaussian probability measures

Sharif Rahman
Journal of Mathematical Analysis and Applications 454 (1) 303 (2017)
DOI: 10.1016/j.jmaa.2017.04.062
See this article

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
See this article

Handbook of Uncertainty Quantification

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

Handbook of Uncertainty Quantification

Khachik Sargsyan
Handbook of Uncertainty Quantification 673 (2017)
DOI: 10.1007/978-3-319-12385-1_22
See this article

Handbook of Uncertainty Quantification

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

Stability-preserving model order reduction for linear stochastic Galerkin systems

Roland Pulch
Journal of Mathematics in Industry 9 (1) (2019)
DOI: 10.1186/s13362-019-0067-6
See this article

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
See this article

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
See this article

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
See this article

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
See this article

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
See this article

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
See this article

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
See this article

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
See this article

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
See this article

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
See this article

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
See this article

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
See this article

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
See this article

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
See this article

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
See this article

Improvement of random coefficient differential models of growth of anaerobic photosynthetic bacteria by combining Bayesian inference and gPC

Julia Calatayud, Juan Carlos Cortés and Marc Jornet
Mathematical Methods in the Applied Sciences (2019)
DOI: 10.1002/mma.5546
See this article

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
See this article

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
See this article

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
See this article

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
See this article

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
See this article

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
See this article

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
See this article

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
See this article

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
See this article

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
See this article

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
See this article

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
See this article

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
See this article

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
See this article

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
See this article

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
See this article

Handbook of Uncertainty Quantification

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

Handbook of Uncertainty Quantification

Bert Debusschere
Handbook of Uncertainty Quantification 1 (2015)
DOI: 10.1007/978-3-319-11259-6_19-1
See this article

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
See this article

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
See this article

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
See this article

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
See this article

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
See this article

A Spline Chaos Expansion

Sharif Rahman
SIAM/ASA Journal on Uncertainty Quantification 8 (1) 27 (2020)
DOI: 10.1137/19M1239702
See this article

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
See this article

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
See this article

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
See this article

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
See this article

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
See this article

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
See this article

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 1 (2020)
DOI: 10.1080/07362994.2020.1733017
See this article

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
See this article

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
See this article

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
See this article

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
See this article

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
See this article

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
See this article

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
See this article

Modeling of Allee effect in biofilm formation via the stochastic bistable Allen–Cahn partial differential equation

Marc Jornet
Stochastic Analysis and Applications 1 (2020)
DOI: 10.1080/07362994.2020.1777163
See this article

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
See this article

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
See this article