Exponential ReLU neural network approximation rates for point and edge singularities (Q6101269)

scientific article; zbMATH DE number 7698615

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English	Exponential ReLU neural network approximation rates for point and edge singularities	scientific article; zbMATH DE number 7698615

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instance of

scholarly article

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title

Exponential ReLU neural network approximation rates for point and edge singularities (English)

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Foundations of Computational Mathematics

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publication date

20 June 2023

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full work available at URL

https://arxiv.org/abs/2010.12217

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zbMATH Keywords

neural networks

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finite element methods

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exponential convergence

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analytic regularity

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singularities

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electron structure

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MaRDI profile type

MaRDI publication profile

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cites work

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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

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Regularite gevrey pour le probleme de dirichlet dans des domaines a singularites coniques

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The Mathematical Theory of Finite Element Methods

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ANALYTIC REGULARITY FOR LINEAR ELLIPTIC SYSTEMS IN POLYGONS AND POLYHEDRA

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Nonlinear approximation and (deep) ReLU networks

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

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Asymptotic regularity of solutions to Hartree-Fock equations with Coulomb potential

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Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni in $n$ variabili

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

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Regularity of the solutions for elliptic problems on nonsmooth domains in ℝ<sup>3</sup>, Part I: countably normed spaces on polyhedral domains

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Regularity of the solutions for elliptic problems on nonsmooth domains in ℝ<sup>3</sup>. Part II: Regularity in neighbourhoods of edges

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Analytic regularity of Stokes flow on polygonal domains in countably weighted Sobolev spaces

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Solving many-electron Schrödinger equation using deep neural networks

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Relu Deep Neural Networks and Linear Finite Elements

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Proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients

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QTT-finite-element approximation for multiscale problems. I: Model problems in one dimension

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Quantized tensor-structured finite elements for second-order elliptic PDEs in two dimensions

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Solutions of Hartree-Fock equations for Coulomb systems

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Tensor rank bounds for point singularities in $\mathbb{R}^3$

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Analytic Regularity for the Incompressible Navier--Stokes Equations in Polygons

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Q3560019

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The partition of unity finite element method: basic theory and applications

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Exponential convergence for hp-version and spectral finite element methods for elliptic problems in polyhedra

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Error bounds for approximations with deep ReLU networks

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Identifiers

zbMATH Open document ID

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10.1007/s10208-022-09565-9

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:6101269