Approximation rates for neural networks with encodable weights in smoothness spaces
From MaRDI portal
Publication:2055067
DOI10.1016/j.neunet.2020.11.010zbMath1475.68314arXiv2006.16822OpenAlexW3107277102WikidataQ104456454 ScholiaQ104456454MaRDI QIDQ2055067
Publication date: 3 December 2021
Published in: Neural Networks (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2006.16822
Artificial neural networks and deep learning (68T07) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Rate of convergence, degree of approximation (41A25)
Related Items
Interpolation and approximation via momentum ResNets and neural ODEs ⋮ Stationary Density Estimation of Itô Diffusions Using Deep Learning ⋮ Convergence of Physics-Informed Neural Networks Applied to Linear Second-Order Elliptic Interface Problems ⋮ A deep learning approach to Reduced Order Modelling of parameter dependent partial differential equations ⋮ Imaging conductivity from current density magnitude using neural networks* ⋮ Construction and approximation for a class of feedforward neural networks with sigmoidal function ⋮ Simultaneous neural network approximation for smooth functions ⋮ On the approximation of functions by tanh neural networks ⋮ Randomized neural network with Petrov-Galerkin methods for solving linear and nonlinear partial differential equations ⋮ Mesh-informed neural networks for operator learning in finite element spaces ⋮ Approximation error for neural network operators by an averaged modulus of smoothness ⋮ Solving Elliptic Problems with Singular Sources Using Singularity Splitting Deep Ritz Method ⋮ Friedrichs Learning: Weak Solutions of Partial Differential Equations via Deep Learning ⋮ A Rate of Convergence of Weak Adversarial Neural Networks for the Second Order Parabolic PDEs ⋮ Error analysis of deep Ritz methods for elliptic equations ⋮ Convergence Analysis of a Quasi-Monte CarloBased Deep Learning Algorithm for Solving Partial Differential Equations ⋮ Improved Analysis of PINNs: Alleviate the CoD for Compositional Solutions ⋮ Convergence Analysis of the Deep Galerkin Method for Weak Solutions ⋮ Neural Control of Parametric Solutions for High-Dimensional Evolution PDEs ⋮ Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Approximation results for neural network operators activated by sigmoidal functions
- Multivariate neural network operators with sigmoidal activation functions
- Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
- Approximation by superposition of sigmoidal and radial basis functions
- Lower bounds for approximation by MLP neural networks
- Approximation and estimation bounds for artificial neural networks
- Provable approximation properties for deep neural networks
- The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
- DGM: a deep learning algorithm for solving partial differential equations
- Optimal approximation of piecewise smooth functions using deep ReLU neural networks
- Nonparametric regression using deep neural networks with ReLU activation function
- Error bounds for approximations with deep ReLU networks
- Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations
- Lectures on Pseudo-Differential Operators: Regularity Theorems and Applications to Non-Elliptic Problems. (MN-24)
- Deep learning in high dimension: Neural network expression rates for generalized polynomial chaos expansions in UQ
- A Multivariate Faa di Bruno Formula with Applications
- Solving high-dimensional partial differential equations using deep learning
- Optimal Approximation with Sparsely Connected Deep Neural Networks
- Deep ReLU networks and high-order finite element methods
- Error bounds for approximations with deep ReLU neural networks in Ws,p norms
- Better Approximations of High Dimensional Smooth Functions by Deep Neural Networks with Rectified Power Units
- A Single Hidden Layer Feedforward Network with Only One Neuron in the Hidden Layer Can Approximate Any Univariate Function
- The Mathematical Theory of Finite Element Methods
- Nonlinear partial differential equations with applications
- Approximation by superpositions of a sigmoidal function
- A practical guide to splines.