Deep learning in high dimension: neural network expression rates for generalized polynomial chaos expansions in UQ

A deep learning approach to estimate stress distribution: a fast and accurate surrogate of finite-element analysis

(2018) Liang Liang et al.   Journal of the Royal Society Interface

Shape Holomorphy of the Stationary Navier--Stokes Equations

(2018) Albert Cohen et al.   SIAM JOURNAL ON MATHEMATICAL ANALYSIS

Multilevel higher-order quasi-Monte Carlo Bayesian estimation

(2017) Josef Dick et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

Error bounds for approximations with deep ReLU networks

(2017) Dmitry Yarotsky   NEURAL NETWORKS

Fully Discrete Approximation of Parametric and Stochastic Elliptic PDEs

(2017) Markus Bachmayr et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Deep vs. shallow networks: An approximation theory perspective

(2016) H. N. Mhaskar et al.   Analysis and Applications

Sparse polynomial approximation of parametric elliptic PDEs. Part I: affine coefficients

(2016) Markus Bachmayr et al.   ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE

Machine learning-based 3-D geometry reconstruction and modeling of aortic valve deformation using 3-D computed tomography images

(2016) Liang Liang et al.   International Journal for Numerical Methods in Biomedical Engineering

Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs

(2015) Abdellah Chkifa et al.   JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES

Approximation of high-dimensional parametric PDEs

(2015) Albert Cohen et al.   ACTA NUMERICA

High-Dimensional Adaptive Sparse Polynomial Interpolation and Applications to Parametric PDEs

(2013) Abdellah Chkifa et al.   FOUNDATIONS OF COMPUTATIONAL MATHEMATICS

Convergence Rates of Multilevel and Sparse Tensor Approximations for a Random Elliptic PDE

(2013) Claude Jeffrey Gittelson   SIAM JOURNAL ON NUMERICAL ANALYSIS

Sparse deterministic approximation of Bayesian inverse problems

(2012) C Schwab et al.   INVERSE PROBLEMS

ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S

(2011) ALBERT COHEN et al.   Analysis and Applications

Convergence Rates of Best N-term Galerkin Approximations for a Class of Elliptic sPDEs

(2010) Albert Cohen et al.   FOUNDATIONS OF COMPUTATIONAL MATHEMATICS

Inverse problems: A Bayesian perspective

(2010) A. M. Stuart   ACTA NUMERICA