Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs
ESAIM: M2AN, 47 1 (2013) 253-280
Published online: 2012-11-29
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):
Error analysis of kernel/GP methods for nonlinear and parametric PDEs
Pau Batlle, Yifan Chen, Bamdad Hosseini, Houman Owhadi and Andrew M. StuartJournal of Computational Physics 520 113488 (2025)
https://doi.org/10.1016/j.jcp.2024.113488
Optimal ANOVA-Based Emulators of Models With(out) Derivatives
Matieyendou LamboniStats 8 (1) 24 (2025)
https://doi.org/10.3390/stats8010024
Bayesian inversion for electrical impedance tomography by sparse interpolation
Quang Huy Pham and Viet Ha HoangInverse Problems and Imaging 19 (5) 1037 (2025)
https://doi.org/10.3934/ipi.2025007
Kernel methods are competitive for operator learning
Pau Batlle, Matthieu Darcy, Bamdad Hosseini and Houman OwhadiJournal of Computational Physics 496 112549 (2024)
https://doi.org/10.1016/j.jcp.2023.112549
A kernel framework for learning differential equations and their solution operators
Da Long, Nicole Mrvaljević, Shandian Zhe and Bamdad HosseiniPhysica D: Nonlinear Phenomena 460 134095 (2024)
https://doi.org/10.1016/j.physd.2024.134095
25 419 (2024)
https://doi.org/10.1016/bs.hna.2024.05.009
Algorithm 1040: The Sparse Grids Matlab Kit - a Matlab implementation of sparse grids for high-dimensional function approximation and uncertainty quantification
Chiara Piazzola and Lorenzo TamelliniACM Transactions on Mathematical Software 50 (1) 1 (2024)
https://doi.org/10.1145/3630023
Learning Homogenization for Elliptic Operators
Kaushik Bhattacharya, Nikola B. Kovachki, Aakila Rajan, Andrew M. Stuart and Margaret TrautnerSIAM Journal on Numerical Analysis 62 (4) 1844 (2024)
https://doi.org/10.1137/23M1585015
Operator Learning Using Random Features: A Tool for Scientific Computing
Nicholas H. Nelsen and Andrew M. StuartSIAM Review 66 (3) 535 (2024)
https://doi.org/10.1137/24M1648703
Collocation approximation by deep neural ReLU networks for parametric and stochastic PDEs with lognormal inputs
Dung DinhSbornik: Mathematics 214 (4) 479 (2023)
https://doi.org/10.4213/sm9791e
Коллокационная аппроксимация глубокими $\mathrm{ReLU}$-нейронными сетями решений параметрических и стохастических уравнений с частными производными c логнормальными входами
Dung DinhМатематический сборник 214 (4) 38 (2023)
https://doi.org/10.4213/sm9791
Sparse Polynomial Approximations for Affine Parametric Saddle Point Problems
Peng Chen and Omar GhattasVietnam Journal of Mathematics 51 (1) 151 (2023)
https://doi.org/10.1007/s10013-022-00584-1
Trace Class in Separable Reflexive Banach Spaces, Lidskii Theorem
Mykola YaremenkoEQUATIONS 2 123 (2022)
https://doi.org/10.37394/232021.2022.2.19
High-Dimensional Optimization and Probability
Ben Adcock, Juan M. Cardenas, Nick Dexter and Sebastian MoragaSpringer Optimization and Its Applications, High-Dimensional Optimization and Probability 191 9 (2022)
https://doi.org/10.1007/978-3-031-00832-0_2
Shape Holomorphy of the Calderón Projector for the Laplacian in $${\mathbb {R}}^2$$
Fernando Henríquez and Christoph SchwabIntegral Equations and Operator Theory 93 (4) (2021)
https://doi.org/10.1007/s00020-021-02653-5
Nonlinear methods for model reduction
Andrea Bonito, Albert Cohen, Ronald DeVore, et al.ESAIM: Mathematical Modelling and Numerical Analysis 55 (2) 507 (2021)
https://doi.org/10.1051/m2an/2020057
The Random Feature Model for Input-Output Maps between Banach Spaces
Nicholas H. Nelsen and Andrew M. StuartSIAM Journal on Scientific Computing 43 (5) A3212 (2021)
https://doi.org/10.1137/20M133957X
Model Reduction And Neural Networks For Parametric PDEs
Kaushik Bhattacharya, Bamdad Hosseini, Nikola B. Kovachki and Andrew M. StuartThe SMAI journal of computational mathematics 7 121 (2021)
https://doi.org/10.5802/smai-jcm.74
Polynomial Approximation of Anisotropic Analytic Functions of Several Variables
Andrea Bonito, Ronald DeVore, Diane Guignard, Peter Jantsch and Guergana PetrovaConstructive Approximation 53 (2) 319 (2021)
https://doi.org/10.1007/s00365-020-09511-4
Sparse-grid polynomial interpolation approximation and integration for parametric and stochastic elliptic PDEs with lognormal inputs
Dinh DũngESAIM: Mathematical Modelling and Numerical Analysis 55 (3) 1163 (2021)
https://doi.org/10.1051/m2an/2021017
A fully adaptive multilevel stochastic collocation strategy for solving elliptic PDEs with random data
J. Lang, R. Scheichl and D. SilvesterJournal of Computational Physics 419 109692 (2020)
https://doi.org/10.1016/j.jcp.2020.109692
Convergence rates of high dimensional Smolyak quadrature
Jakob Zech and Christoph SchwabESAIM: Mathematical Modelling and Numerical Analysis 54 (4) 1259 (2020)
https://doi.org/10.1051/m2an/2020003
Regularity and sparse approximation of the recursive first moment equations for the lognormal Darcy problem
Francesca Bonizzoni and Fabio NobileComputers & Mathematics with Applications 80 (12) 2925 (2020)
https://doi.org/10.1016/j.camwa.2020.10.014
A mixed ℓ1 regularization approach for sparse simultaneous approximation of parameterized PDEs
Nick Dexter, Hoang Tran and Clayton WebsterESAIM: Mathematical Modelling and Numerical Analysis 53 (6) 2025 (2019)
https://doi.org/10.1051/m2an/2019048
Linear collective collocation approximation for parametric and stochastic elliptic PDEs
Dinh DũngSbornik: Mathematics 210 (4) 565 (2019)
https://doi.org/10.1070/SM9068
IGA-based multi-index stochastic collocation for random PDEs on arbitrary domains
Joakim Beck, Lorenzo Tamellini and Raúl TemponeComputer Methods in Applied Mechanics and Engineering 351 330 (2019)
https://doi.org/10.1016/j.cma.2019.03.042
Multilevel approximation of parametric and stochastic PDES
Jakob Zech, Dinh Dũng and Christoph SchwabMathematical Models and Methods in Applied Sciences 29 (09) 1753 (2019)
https://doi.org/10.1142/S0218202519500349
Линейная совместная коллокационная аппроксимация для параметрических и стохастических эллиптических дифференциальных уравнений с частными производными
Dung DinhМатематический сборник 210 (4) 103 (2019)
https://doi.org/10.4213/sm9068
A Posteriori Error Estimation for the Stochastic Collocation Finite Element Method
Diane Guignard and Fabio NobileSIAM Journal on Numerical Analysis 56 (5) 3121 (2018)
https://doi.org/10.1137/17M1155454
Shape Holomorphy of the Stationary Navier--Stokes Equations
Albert Cohen, Christoph Schwab and Jakob ZechSIAM Journal on Mathematical Analysis 50 (2) 1720 (2018)
https://doi.org/10.1137/16M1099406
Quasi--Monte Carlo Integration for Affine-Parametric, Elliptic PDEs: Local Supports and Product Weights
Robert N. Gantner, Lukas Herrmann and Christoph SchwabSIAM Journal on Numerical Analysis 56 (1) 111 (2018)
https://doi.org/10.1137/16M1082597
A multiscale method for semi-linear elliptic equations with localized uncertainties and non-linearities
Anthony Nouy and Florent PledESAIM: Mathematical Modelling and Numerical Analysis 52 (5) 1763 (2018)
https://doi.org/10.1051/m2an/2018025
Handbook of Uncertainty Quantification
Peng Chen and Christoph SchwabHandbook of Uncertainty Quantification 937 (2017)
https://doi.org/10.1007/978-3-319-12385-1_70
Analysis of quasi-optimal polynomial approximations for parameterized PDEs with deterministic and stochastic coefficients
Hoang Tran, Clayton G. Webster and Guannan ZhangNumerische Mathematik 137 (2) 451 (2017)
https://doi.org/10.1007/s00211-017-0878-6
Handbook of Uncertainty Quantification
Max Gunzburger, Clayton G. Webster and Guannan ZhangHandbook of Uncertainty Quantification 717 (2017)
https://doi.org/10.1007/978-3-319-12385-1_29
Electromagnetic wave scattering by random surfaces: Shape holomorphy
Carlos Jerez-Hanckes, Christoph Schwab and Jakob ZechMathematical Models and Methods in Applied Sciences 27 (12) 2229 (2017)
https://doi.org/10.1142/S0218202517500439
Data Assimilation in Reduced Modeling
Peter Binev, Albert Cohen, Wolfgang Dahmen, et al.SIAM/ASA Journal on Uncertainty Quantification 5 (1) 1 (2017)
https://doi.org/10.1137/15M1025384
Compressed Sensing and its Applications
Ben Adcock, Simone Brugiapaglia and Clayton G. WebsterApplied and Numerical Harmonic Analysis, Compressed Sensing and its Applications 93 (2017)
https://doi.org/10.1007/978-3-319-69802-1_3
Sparse polynomial approximation of parametric elliptic PDEs. Part I: affine coefficients
Markus Bachmayr, Albert Cohen and Giovanni MiglioratiESAIM: Mathematical Modelling and Numerical Analysis 51 (1) 321 (2017)
https://doi.org/10.1051/m2an/2016045
Convergence of quasi-optimal sparse-grid approximation of Hilbert-space-valued functions: application to random elliptic PDEs
F. Nobile, L. Tamellini and R. TemponeNumerische Mathematik 134 (2) 343 (2016)
https://doi.org/10.1007/s00211-015-0773-y
Tensor train approximation of moment equations for elliptic equations with lognormal coefficient
F. Bonizzoni, F. Nobile and D. KressnerComputer Methods in Applied Mechanics and Engineering 308 349 (2016)
https://doi.org/10.1016/j.cma.2016.05.026
Numerical study of a parametric parabolic equation and a related inverse boundary value problem
Lauri MustonenInverse Problems 32 (10) 105008 (2016)
https://doi.org/10.1088/0266-5611/32/10/105008
Sparse Adaptive Tensor Galerkin Approximations of Stochastic PDE-Constrained Control Problems
Angela Kunoth and Christoph SchwabSIAM/ASA Journal on Uncertainty Quantification 4 (1) 1034 (2016)
https://doi.org/10.1137/15M1041390
A dynamically adaptive sparse grids method for quasi-optimal interpolation of multidimensional functions
Miroslav K. Stoyanov and Clayton G. WebsterComputers & Mathematics with Applications 71 (11) 2449 (2016)
https://doi.org/10.1016/j.camwa.2015.12.045
Sparse Grids and Applications - Stuttgart 2014
Peng Chen and Christoph SchwabLecture Notes in Computational Science and Engineering, Sparse Grids and Applications - Stuttgart 2014 109 1 (2016)
https://doi.org/10.1007/978-3-319-28262-6_1
Sparse-grid, reduced-basis Bayesian inversion: Nonaffine-parametric nonlinear equations
Peng Chen and Christoph SchwabJournal of Computational Physics 316 470 (2016)
https://doi.org/10.1016/j.jcp.2016.02.055
Hyperbolic cross approximation in infinite dimensions
Dinh Dũng and Michael GriebelJournal of Complexity 33 55 (2016)
https://doi.org/10.1016/j.jco.2015.09.006
Approximation of high-dimensional parametric PDEs
Albert Cohen and Ronald DeVoreActa Numerica 24 1 (2015)
https://doi.org/10.1017/S0962492915000033
Encyclopedia of Applied and Computational Mathematics
Christoph SchwabEncyclopedia of Applied and Computational Mathematics 903 (2015)
https://doi.org/10.1007/978-3-540-70529-1_526
Handbook of Uncertainty Quantification
Max Gunzburger, Clayton G. Webster and Guannan ZhangHandbook of Uncertainty Quantification 1 (2015)
https://doi.org/10.1007/978-3-319-11259-6_29-1
Handbook of Uncertainty Quantification
Peng Chen and Christoph SchwabHandbook of Uncertainty Quantification 1 (2015)
https://doi.org/10.1007/978-3-319-11259-6_70-1
Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs
Abdellah Chkifa, Albert Cohen, Giovanni Migliorati, Fabio Nobile and Raul TemponeESAIM: Mathematical Modelling and Numerical Analysis 49 (3) 815 (2015)
https://doi.org/10.1051/m2an/2014050
Sampling Theory, a Renaissance
Albert Cohen and Abdellah ChkifaApplied and Numerical Harmonic Analysis, Sampling Theory, a Renaissance 437 (2015)
https://doi.org/10.1007/978-3-319-19749-4_12
Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs
Abdellah Chkifa, Albert Cohen and Christoph SchwabJournal de Mathématiques Pures et Appliquées 103 (2) 400 (2015)
https://doi.org/10.1016/j.matpur.2014.04.009
Approximate methods for stochastic eigenvalue problems
H. Hakula, V. Kaarnioja and M. LaaksonenApplied Mathematics and Computation 267 664 (2015)
https://doi.org/10.1016/j.amc.2014.12.112
Hybrid Stochastic Finite Element Method for Mechanical Vibration Problems
Harri Hakula and Mikael LaaksonenShock and Vibration 2015 1 (2015)
https://doi.org/10.1155/2015/812069
A convergent adaptive stochastic Galerkin finite element method with quasi-optimal spatial meshes
Martin Eigel, Claude Jeffrey Gittelson, Christoph Schwab and Elmar ZanderESAIM: Mathematical Modelling and Numerical Analysis 49 (5) 1367 (2015)
https://doi.org/10.1051/m2an/2015017
Greedy Algorithms for High-Dimensional Eigenvalue Problems
Eric Cancès, Virginie Ehrlacher and Tony LelièvreConstructive Approximation 40 (3) 387 (2014)
https://doi.org/10.1007/s00365-014-9266-y
Inverse modeling of geochemical and mechanical compaction in sedimentary basins through Polynomial Chaos Expansion
G. Porta, L. Tamellini, V. Lever and M. RivaWater Resources Research 50 (12) 9414 (2014)
https://doi.org/10.1002/2014WR015838
Modeling, Simulation and Optimization of Complex Processes - HPSC 2012
Markus Hansen, Claudia Schillings and Christoph SchwabModeling, Simulation and Optimization of Complex Processes - HPSC 2012 63 (2014)
https://doi.org/10.1007/978-3-319-09063-4_6
Convergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficients
Joakim Beck, Fabio Nobile, Lorenzo Tamellini and Raúl TemponeComputers & Mathematics with Applications 67 (4) 732 (2014)
https://doi.org/10.1016/j.camwa.2013.03.004
Sparsity in Bayesian inversion of parametric operator equations
Cl Schillings and Ch SchwabInverse Problems 30 (6) 065007 (2014)
https://doi.org/10.1088/0266-5611/30/6/065007
Extraction of Quantifiable Information from Complex Systems
Wolfgang Dahmen, Chunyan Huang, Gitta Kutyniok, et al.Lecture Notes in Computational Science and Engineering, Extraction of Quantifiable Information from Complex Systems 102 25 (2014)
https://doi.org/10.1007/978-3-319-08159-5_2
Perturbation Analysis for the Darcy Problem with Log-Normal Permeability
Francesca Bonizzoni and Fabio NobileSIAM/ASA Journal on Uncertainty Quantification 2 (1) 223 (2014)
https://doi.org/10.1137/130949415
High-Dimensional Adaptive Sparse Polynomial Interpolation and Applications to Parametric PDEs
Abdellah Chkifa, Albert Cohen and Christoph SchwabFoundations of Computational Mathematics 14 (4) 601 (2014)
https://doi.org/10.1007/s10208-013-9154-z
On the Lebesgue constant of Leja sequences for the complex unit disk and of their real projection
Moulay Abdellah ChkifaJournal of Approximation Theory 166 176 (2013)
https://doi.org/10.1016/j.jat.2012.11.005
Analytic Regularity and GPC Approximation for Control Problems Constrained by Linear Parametric Elliptic and Parabolic PDEs
Angela Kunoth and Christoph SchwabSIAM Journal on Control and Optimization 51 (3) 2442 (2013)
https://doi.org/10.1137/110847597
A Trust-Region Algorithm with Adaptive Stochastic Collocation for PDE Optimization under Uncertainty
D. P. Kouri, M. Heinkenschloss, D. Ridzal and B. G. van Bloemen WaandersSIAM Journal on Scientific Computing 35 (4) A1847 (2013)
https://doi.org/10.1137/120892362
Sparse, adaptive Smolyak quadratures for Bayesian inverse problems
Claudia Schillings and Christoph SchwabInverse Problems 29 (6) 065011 (2013)
https://doi.org/10.1088/0266-5611/29/6/065011
Complexity analysis of accelerated MCMC methods for Bayesian inversion
Viet Ha Hoang, Christoph Schwab and Andrew M StuartInverse Problems 29 (8) 085010 (2013)
https://doi.org/10.1088/0266-5611/29/8/085010
Uniformly convergent adaptive methods for a class of parametric operator equations
Claude Jeffrey GittelsonESAIM: Mathematical Modelling and Numerical Analysis 46 (6) 1485 (2012)
https://doi.org/10.1051/m2an/2012013