Randomized neural network with Petrov-Galerkin methods for solving linear and nonlinear partial differential equations (Q6058946)

scientific article; zbMATH DE number 7759102

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English	Randomized neural network with Petrov-Galerkin methods for solving linear and nonlinear partial differential equations	scientific article; zbMATH DE number 7759102

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instance of

scholarly article

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title

Randomized neural network with Petrov-Galerkin methods for solving linear and nonlinear partial differential equations (English)

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Communications in Nonlinear Science and Numerical Simulation

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publication date

1 November 2023

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zbMATH Keywords

Petrov-Galerkin method

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randomized neural network

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least-squares method

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space-time approach

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MaRDI profile type

MaRDI publication profile

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cites work

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Least-squares ReLU neural network (LSNN) method for linear advection-reaction equation

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Deep least-squares methods: an unsupervised learning-based numerical method for solving elliptic PDEs

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Deep Nitsche Method: Deep Ritz Method with Essential Boundary Conditions

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Variational physics informed neural networks: the role of quadratures and test functions

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Local extreme learning machines and domain decomposition for solving linear and nonlinear partial differential equations

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The finite element method with Lagrangian multipliers

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Some observations on Babuška and Brezzi theories

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Approximation by superpositions of a sigmoidal function

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Approximation and estimation bounds for artificial neural networks

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Optimal Approximation with Sparsely Connected Deep Neural Networks

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Error bounds for approximations with deep ReLU networks

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Approximation rates for neural networks with encodable weights in smoothness spaces

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Q4136469

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One-dimensional linear advection-diffusion equation: analytical and finite element solutions

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Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs

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Identifiers

zbMATH Open document ID

1525.65128

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Mathematics Subject Classification ID

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10.1016/J.CNSNS.2023.107518

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Sitelinks

Mathematics(1 entry)

mardi Publication:6058946