DOI10.1051/m2an/2012027zbMath1273.65009OpenAlexW2117188967MaRDI QIDQ2836463
Albert Cohen, Christoph Schwab, Abdellah Chkifa, Ronald A. DeVore
Publication date: 3 July 2013
Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1051/m2an/2012027
A fully adaptive multilevel stochastic collocation strategy for solving elliptic PDEs with random data,
A convergent adaptive stochastic Galerkin finite element method with quasi-optimal spatial meshes,
Sparse-grid, reduced-basis Bayesian inversion: nonaffine-parametric nonlinear equations,
Greedy algorithms for high-dimensional non-symmetric linear problems,
Sparse Adaptive Tensor Galerkin Approximations of Stochastic PDE-Constrained Control Problems,
Convergence of quasi-optimal sparse-grid approximation of Hilbert-space-valued functions: Application to random elliptic PDEs,
Convergence of quasi-optimal stochastic Galerkin methods for a class of PDES with random coefficients,
A Posteriori Error Estimation for the Stochastic Collocation Finite Element Method,
Sparse adaptive approximation of high dimensional parametric initial value problems,
IGA-based multi-index stochastic collocation for random PDEs on arbitrary domains,
Polynomial approximation of anisotropic analytic functions of several variables,
Analysis of quasi-optimal polynomial approximations for parameterized PDEs with deterministic and stochastic coefficients,
Electromagnetic wave scattering by random surfaces: Shape holomorphy,
Kolmogorov widths and low-rank approximations of parametric elliptic PDEs,
High-dimensional adaptive sparse polynomial interpolation and applications to parametric PDEs,
Sparse polynomial approximations for affine parametric saddle point problems,
Collocation approximation by deep neural ReLU networks for parametric and stochastic PDEs with lognormal inputs,
Quasi--Monte Carlo Integration for Affine-Parametric, Elliptic PDEs: Local Supports and Product Weights,
Kernel methods are competitive for operator learning,
Polynomial approximation via compressed sensing of high-dimensional functions on lower sets,
Stochastic Methods for Solving High-Dimensional Partial Differential Equations,
Convergence rates of high dimensional Smolyak quadrature,
Shape Holomorphy of the Stationary Navier--Stokes Equations,
Regularity and sparse approximation of the recursive first moment equations for the lognormal Darcy problem,
Towards optimal sampling for learning sparse approximation in high dimensions,
A multiscale method for semi-linear elliptic equations with localized uncertainties and non-linearities,
Greedy algorithms for high-dimensional eigenvalue problems,
Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs,
Approximate methods for stochastic eigenvalue problems,
Sparse-grid polynomial interpolation approximation and integration for parametric and stochastic elliptic PDEs with lognormal inputs,
A dynamically adaptive sparse grids method for quasi-optimal interpolation of multidimensional functions,
On the Stability of Polynomial Interpolation Using Hierarchical Sampling,
Hyperbolic cross approximation in infinite dimensions,
Shape holomorphy of the Calderón projector for the Laplacian in \(\mathbb{R}^2\),
Linear collective collocation approximation for parametric and stochastic elliptic PDEs,
A mixed ℓ1 regularization approach for sparse simultaneous approximation of parameterized PDEs,
Model reduction and neural networks for parametric PDEs,
The Random Feature Model for Input-Output Maps between Banach Spaces,
Multilevel approximation of parametric and stochastic PDES,
Tensor train approximation of moment equations for elliptic equations with lognormal coefficient,
Nonlinear methods for model reduction,
Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs,
Efficient Resolution of Anisotropic Structures,
Data Assimilation in Reduced Modeling
