Exponential ReLU DNN expression of holomorphic maps in high dimension
type: Item
instance of: scholarly article
title: Exponential ReLU DNN expression of holomorphic maps in high dimension
zbMATH Open document ID: 1500.41008
author: Joost A. A. Opschoor
author: Christoph Schwab
author: J. Zech
published in: Constructive Approximation
publication date: 2022-03-21T00:00:00Z
Mathematics Subject Classification ID: 41A46
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 68T07
zbMATH DE Number: 7493725
zbMATH Keywords: deep ReLU neural networks
zbMATH Keywords: approximation rates
zbMATH Keywords: exponential convergence
zbMATH Keywords: Gevrey regularity
MaRDI profile type: Publication
full work available at URL: s00365-021-09542-5
OpenAlex ID: W3161792008
Wikidata QID: Q115607850
cites work: Optimal Approximation with Sparsely Connected Deep Neural Networks
cites work: Polynomial approximation of anisotropic analytic functions of several variables
cites work: Q4842676
cites work: Approximation by Ridge functions and neural networks with one hidden layer
cites work: Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs
cites work: Convergence rates of best \(N\)-term Galerkin approximations for a class of elliptic SPDEs
cites work: EXPONENTIAL CONVERGENCE OF hp-FEM FOR MAXWELL EQUATIONS WITH WEIGHTED REGULARIZATION IN POLYGONAL DOMAINS
cites work: Q4095322
cites work: Q5824493
cites work: Exponential convergence in \(H^1\) of \textit{hp}-FEM for Gevrey regularity with isotropic singularities
cites work: Gevrey class regularity for the solutions of the Navier-Stokes equations
cites work: Deep neural network expression of posterior expectations in Bayesian PDE inversion
cites work: Multilayer feedforward networks are universal approximators
cites work: Better Approximations of High Dimensional Smooth Functions by Deep Neural Networks with Rectified Power Units
cites work: Approximation by superposition of sigmoidal and radial basis functions
cites work: Approximation properties of a multilayered feedforward artificial neural network
cites work: An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
cites work: Deep ReLU networks and high-order finite element methods
cites work: Optimal approximation of piecewise smooth functions using deep ReLU neural networks
cites work: Q4938227
cites work: Q4274290
cites work: Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling
cites work: \(hp\)-dGFEM for second order elliptic problems in polyhedra. II: Exponential convergence
cites work: Deep learning in high dimension: Neural network expression rates for generalized polynomial chaos expansions in UQ
cites work: Analysis of quasi-optimal polynomial approximations for parameterized PDEs with deterministic and stochastic coefficients
cites work: Exponential convergence of the deep neural network approximation for analytic functions
cites work: Error bounds for approximations with deep ReLU networks
cites work: An upper estimate of integral points in real simplices with an application to singularity theory
cites work: Multilevel approximation of parametric and stochastic PDES
cites work: Convergence rates of high dimensional Smolyak quadrature
DOI: 10.1007/S00365-021-09542-5
Recommended article: Exponential ReLU neural network approximation rates for point and edge singularities
Recommended article: Deep Learning in High Dimension: Neural Network Expression Rates for Analytic Functions in \(\pmb{L^2(\mathbb{R}^d,\gamma_d)}\)
Recommended article: Exponential convergence of the deep neural network approximation for analytic functions
Recommended article: Holomorphic feedforward networks
Recommended article: Deep ReLU neural networks in high-dimensional approximation
Recommended article: Deep Neural Networks with ReLU-Sine-Exponential Activations Break Curse of Dimensionality in Approximation on Hölder Class
Recommended article: Nonlinear approximation and (deep) ReLU networks
Recommended article: Deep ReLU neural network approximation in Bochner spaces and applications to parametric PDEs
Recommended article: Deep learning in high dimension: Neural network expression rates for generalized polynomial chaos expansions in UQ
Recommended article: Exponential convergence for high-order recurrent neural networks with a class of general activation functions
description: scientific article; zbMATH DE number 7493725