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Deep ReLU networks and high-order finite element methods. II: Chebyšev emulation (Q6585367)

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scientific article; zbMATH DE number 7894795

Language	Label	Description	Also known as
English	Deep ReLU networks and high-order finite element methods. II: Chebyšev emulation	scientific article; zbMATH DE number 7894795

Statements

scholarly article

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Deep ReLU networks and high-order finite element methods. II: Chebyšev emulation (English)

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Joost A. A. Opschoor

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Christoph Schwab

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publication date

9 August 2024

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zbMATH Keywords

neural networks

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\(hp\)-finite element methods

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Chebyšev expansions

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MaRDI profile type

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The Mathematical Theory of Finite Element Methods

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Exponential convergence of {\(hp\)} quadrature for integral operators with Gevrey kernels

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Nonlinear approximation and (deep) ReLU networks

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On the approximation of functions by tanh neural networks

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Neural network approximation

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

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Exponential convergence in \(H^1\) of \textit{hp}-FEM for Gevrey regularity with isotropic singularities

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On the Markov inequality in \(L^ p\)-spaces

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

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Constructive deep ReLU neural network approximation

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On some generalizations of a theorem of A. Markoff

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A Framework for the Construction of Upper Bounds on the Number of Affine Linear Regions of ReLU Feed-Forward Neural Networks

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Adaptive activation functions accelerate convergence in deep and physics-informed neural networks

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Efficient approximation of solutions of parametric linear transport equations by ReLU DNNs

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De Rham compatible deep neural network FEM

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Interpolation Theory

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On the decay rate of Chebyshev coefficients

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Exponential ReLU neural network approximation rates for point and edge singularities

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Deep ReLU Networks Overcome the Curse of Dimensionality for Generalized Bandlimited Functions

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Deep ReLU networks and high-order finite element methods

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Exponential ReLU DNN expression of holomorphic maps in high dimension

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On the degree of nonlinear spline approximation in Besov-Sobolev spaces

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Optimal approximation of piecewise smooth functions using deep ReLU neural networks

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

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Deep Network Approximation Characterized by Number of Neurons

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Neural network approximation: three hidden layers are enough

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An exact mapping from ReLU networks to spiking neural networks

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Is Gauss Quadrature Better than Clenshaw–Curtis?

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Error bounds for approximations with deep ReLU networks

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Computers & Mathematics with Applications

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Identifiers

10.1016/j.camwa.2024.06.008

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:6585367

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