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Generalization of PINNs for elliptic interface problems - MaRDI portal

Generalization of PINNs for elliptic interface problems (Q6595451)

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scientific article; zbMATH DE number 7903701

Language	Label	Description	Also known as
English	Generalization of PINNs for elliptic interface problems	scientific article; zbMATH DE number 7903701

Statements

scholarly article

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Generalization of PINNs for elliptic interface problems (English)

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Applied Mathematics Letters

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publication date

30 August 2024

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zbMATH Keywords

PDE solver

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physics-informed neural network

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generalization

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MaRDI profile type

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A hybrid method for moving interface problems with application to the Hele-Shaw flow

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

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A Petrov-Galerkin finite element interface method for interface problems with Bloch-periodic boundary conditions and its application in phononic crystals

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Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

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Neural‐network‐based approximations for solving partial differential equations

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Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations

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An efficient neural network method with plane wave activation functions for solving Helmholtz equation

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

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Estimates on the generalization error of physics-informed neural networks for approximating PDEs

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Convergence Rate Analysis for Deep Ritz Method

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A Rate of Convergence of Physics Informed Neural Networks for the Linear Second Order Elliptic PDEs

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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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When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?

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DGM: a deep learning algorithm for solving partial differential equations

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Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs

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

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Nonparametric regression using deep neural networks with ReLU activation function

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Finite Neuron Method and Convergence Analysis

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Identifiers

zbMATH Open document ID

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10.1016/j.aml.2024.109175

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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:6595451

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