Simultaneous neural network approximation for smooth functions (Q6052416)

scientific article; zbMATH DE number 7751022

Language	Label	Description	Also known as
English	Simultaneous neural network approximation for smooth functions	scientific article; zbMATH DE number 7751022

Statements

instance of

scholarly article

0 references

title

Simultaneous neural network approximation for smooth functions (English)

0 references

0 references

0 references

0 references

17 October 2023

0 references

full work available at URL

https://arxiv.org/abs/2109.00161

0 references

zbMATH Keywords

deep neural networks

0 references

Sobolev norm

0 references

ReLU\(^k\) activation functions

0 references

approximation theory

0 references

MaRDI profile type

MaRDI publication profile

0 references

cites work

Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of Black--Scholes Partial Differential Equations

0 references

Optimal Approximation with Sparsely Connected Deep Neural Networks

0 references

Nonlinear approximation and (deep) ReLU networks

0 references

Neural network approximation

0 references

Optimal nonlinear approximation

0 references

DNN expression rate analysis of high-dimensional PDEs: application to option pricing

0 references

Numerical solution of the parametric diffusion equation by deep neural networks

0 references

Approximation spaces of deep neural networks

0 references

SelectNet: self-paced learning for high-dimensional partial differential equations

0 references

Error bounds for approximations with deep ReLU neural networks in Ws,p norms

0 references

Approximation rates for neural networks with encodable weights in smoothness spaces

0 references

Solving high-dimensional partial differential equations using deep learning

0 references

Machine learning for prediction with missing dynamics

0 references

Relu Deep Neural Networks and Linear Finite Elements

0 references

Solving parametric PDE problems with artificial neural networks

0 references

PDE-Net 2.0: learning PDEs from data with a numeric-symbolic hybrid deep network

0 references

Deep Network Approximation for Smooth Functions

0 references

Model Reduction with Memory and the Machine Learning of Dynamical Systems

0 references

A mean field view of the landscape of two-layer neural networks

0 references

New Error Bounds for Deep ReLU Networks Using Sparse Grids

0 references

Error bounds for deep ReLU networks using the Kolmogorov-Arnold superposition theorem

0 references

Deep ReLU networks and high-order finite element methods

0 references

Optimal approximation of piecewise smooth functions using deep ReLU neural networks

0 references

Data driven governing equations approximation using deep neural networks

0 references

Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

0 references

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

0 references

Nonlinear approximation via compositions

0 references

Deep Network Approximation Characterized by Number of Neurons

0 references

Deep Network With Approximation Error Being Reciprocal of Width to Power of Square Root of Depth

0 references

Neural network approximation: three hidden layers are enough

0 references

Approximation rates for neural networks with general activation functions

0 references

Theoretical Insights Into the Optimization Landscape of Over-Parameterized Shallow Neural Networks

0 references

A proposal on machine learning via dynamical systems

0 references

Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations

0 references

A priori estimates of the population risk for two-layer neural networks

0 references

The Barron space and the flow-induced function spaces for neural network models

0 references

Exponential convergence of the deep neural network approximation for analytic functions

0 references

Error bounds for approximations with deep ReLU networks

0 references

Identifiers

arXiv ID

2109.00161

0 references

Mathematics Subject Classification ID

0 references

0 references

0 references

0 references

10.1016/J.NEUNET.2022.06.040

0 references

Sitelinks

Mathematics(1 entry)

mardi Publication:6052416