BI-GreenNet: learning Green's functions by boundary integral network

DOI10.1007/s40304-023-00338-6OpenAlexW4327621565MaRDI QIDQ2699491

Yanyan Li

Publication date: 26 April 2023

Published in: Communications in Mathematics and Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2204.13247

zbMATH Keywords

Green's functionboundary integral methodHelmholtz equationPoisson equation

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Green's functions for elliptic equations (35J08) Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs (65N80)

Related Items (1)

Learning domain-independent Green's function for elliptic partial differential equations

Uses Software

• DiffSharp
• ImageNet
• BERT
• DGM
• DeepONet

Cites Work

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• A correction function method for Poisson problems with interface jump conditions
• Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
• Boundary integral equations
• High order matched interface and boundary methods for the Helmholtz equation in media with arbitrarily curved interfaces
• The numerical solution of the Helmholtz equation for wave propagation problems in underwater acoustics
• Some applications of the Greens' function method in mechanics
• Some formulations coupling finite element and integral equation methods for Helmholtz equation and electromagnetism
• A smoothed finite element method for exterior Helmholtz equation in two dimensions
• Multilayer feedforward networks are universal approximators
• The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
• An unfitted finite element method, based on Nitsche's method, for elliptic interface problems.
• Solution of Helmholtz equation in the exterior domain by elementary boundary integral methods
• DGM: a deep learning algorithm for solving partial differential equations
• MIM: a deep mixed residual method for solving high-order partial differential equations
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Hybrid Gauss-Trapezoidal Quadrature Rules
• Neural‐network‐based approximations for solving partial differential equations
• High-Order Corrected Trapezoidal Quadrature Rules for Singular Functions
• An Immersed Interface Method for Incompressible Navier--Stokes Equations
• Green’s Functions with Applications, Second Edition

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