Deep ReLU neural network approximation in Bochner spaces and applications to parametric PDEs (Q6062166)

scientific article; zbMATH DE number 7772613

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English	Deep ReLU neural network approximation in Bochner spaces and applications to parametric PDEs	scientific article; zbMATH DE number 7772613

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instance of

scholarly article

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title

Deep ReLU neural network approximation in Bochner spaces and applications to parametric PDEs (English)

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Journal of Complexity

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publication date

30 November 2023

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full work available at URL

https://arxiv.org/abs/2111.05854

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zbMATH Keywords

high-dimensional approximation in Bochner spaces

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deep ReLU neural networks

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parametric elliptic PDEs with random inputs

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MaRDI profile type

MaRDI publication profile

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cites work

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Sparse polynomial approximation of parametric elliptic PDEs. Part I: affine coefficients

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Q3973919

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Approximation of high-dimensional parametric PDEs

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Convergence rates of best \(N\)-term Galerkin approximations for a class of elliptic SPDEs

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ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S

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Approximation by superpositions of a sigmoidal function

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Sparse-grid polynomial interpolation approximation and integration for parametric and stochastic elliptic PDEs with lognormal inputs

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Erratum to: “Sparse-grid polynomial interpolation approximation and integration for parametric and stochastic elliptic PDEs with lognormal inputs”

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Deep ReLU neural networks in high-dimensional approximation

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Exponential convergence of the deep neural network approximation for analytic functions

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

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Convergence of Sparse Collocation for Functions of Countably Many Gaussian Random Variables (with Application to Elliptic PDEs)

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Deep ReLU network expression rates for option prices in high-dimensional, exponential Lévy models

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Approximation spaces of deep neural networks

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Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions

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Deep neural network approximations for solutions of PDEs based on Monte Carlo algorithms

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

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Deep neural network expression of posterior expectations in Bayesian PDE inversion

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Q5509729

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N-TERM WIENER CHAOS APPROXIMATION RATES FOR ELLIPTIC PDEs WITH LOGNORMAL GAUSSIAN RANDOM INPUTS

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Multilayer feedforward networks are universal approximators

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A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations

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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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A theoretical analysis of deep neural networks and parametric PDEs

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Q3406470

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New Error Bounds for Deep ReLU Networks Using Sparse Grids

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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 UQ: learning deep neural network surrogate models for high dimensional uncertainty quantification

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Error bounds for approximations with deep ReLU networks

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Multilevel approximation of parametric and stochastic PDES

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Identifiers

arXiv ID

2111.05854

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DOI

10.1016/j.jco.2023.101779

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:6062166