A Reduced Order Schwarz Method for Nonlinear Multiscale Elliptic Equations Based on Two-Layer Neural Networks (Q6197994)

scientific article; zbMATH DE number 7806684

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English	A Reduced Order Schwarz Method for Nonlinear Multiscale Elliptic Equations Based on Two-Layer Neural Networks	scientific article; zbMATH DE number 7806684

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instance of

scholarly article

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title

A Reduced Order Schwarz Method for Nonlinear Multiscale Elliptic Equations Based on Two-Layer Neural Networks (English)

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Journal of Computational Mathematics

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publication date

20 February 2024

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full work available at URL

https://arxiv.org/abs/2111.02280

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zbMATH Keywords

nonlinear homogenization

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multiscale elliptic problem

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neural networks

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domain decomposition

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MaRDI profile type

MaRDI publication profile

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cites work

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Randomized Sampling for Basis Function Construction in Generalized Finite Element Methods

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A Low-Rank Schwarz Method for Radiative Transfer Equation With Heterogeneous Scattering Coefficient

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

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Controlling oscillations in high-order discontinuous Galerkin schemes using artificial viscosity tuned by neural networks

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The heterogeneous multiscale methods

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Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations

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The Barron space and the flow-induced function spaces for neural network models

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Multiscale Finite Element Methods

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Convergence of a Nonconforming Multiscale Finite Element Method

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Periodic homogenisation of certain fully nonlinear partial differential equations

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BCR-net: A neural network based on the nonstandard wavelet form

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Identifiers

arXiv ID

2111.02280

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DOI

10.4208/jcm.2204-m2021-0311

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:6197994