Convergence of Physics-Informed Neural Networks Applied to Linear Second-Order Elliptic Interface Problems (Q5887902)

scientific article; zbMATH DE number 7677220

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English	Convergence of Physics-Informed Neural Networks Applied to Linear Second-Order Elliptic Interface Problems	scientific article; zbMATH DE number 7677220

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instance of

scholarly article

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title

Convergence of Physics-Informed Neural Networks Applied to Linear Second-Order Elliptic Interface Problems (English)

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Communications in Computational Physics

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publication date

21 April 2023

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full work available at URL

https://arxiv.org/abs/2203.03407

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zbMATH Keywords

elliptic interface problems

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generalization errors

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convergence analysis

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neural networks

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describes a project that uses

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MaRDI publication profile

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cites work

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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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A moment-of-fluid method for diffusion equations on irregular domains in multi-material systems

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The immersed boundary method

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Solving elliptic problems with discontinuities on irregular domains -- the Voronoi interface method

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On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs

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Universal approximation bounds for superpositions of a sigmoidal function

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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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Consistency of Lipschitz Learning with Infinite Unlabeled Data and Finite Labeled Data

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Approximation by superpositions of a sigmoidal function

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Approximation rates for neural networks with encodable weights in smoothness spaces

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On the approximation of functions by tanh neural networks

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Neural network approximation: three hidden layers are enough

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The finite element method for elliptic equations with discontinuous coefficients

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On the poisson equation with intersecting interfaces

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Identifiers

DOI

10.4208/cicp.OA-2022-0218

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:5887902