Learning scattering waves via coupling physics-informed neural networks and their convergence analysis
DOI10.1016/j.cam.2024.115874zbMATH Open1542.65173MaRDI QIDQ6567300
Publication date: 4 July 2024
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
convergence analysisHelmholtz equationscattering problemDirichlet-to-Neumann conditioncoupling physics-informed neural networks
Computational learning theory (68Q32) Artificial neural networks and deep learning (68T07) Numerical optimization and variational techniques (65K10) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)
Cites Work
- Unnamed Item
- Unnamed Item
- Adaptive perfectly matched layer method for multiple scattering problems
- Error analysis of the DtN-FEM for the scattering problem in acoustics via Fourier analysis
- Analysis of multiple scattering iterations for high-frequency scattering problems. II: The three-dimensional scalar case
- Analysis of continuous formulations underlying the computation of time- harmonic acoustics in exterior domains
- Inverse acoustic and electromagnetic scattering theory.
- The Helmholtz equation in heterogeneous media: a priori bounds, well-posedness, and resonances
- A highly accurate finite-difference method with minimum dispersion error for solving the Helmholtz equation
- On nonreflecting boundary conditions
- An efficient iterative method for solving multiple scattering in locally inhomogeneous media
- DGM: a deep learning algorithm for solving partial differential equations
- Seamless integration of elliptic Dirichlet-to-Neumann boundary condition and high order spectral element method for scattering problem
- Data-driven deep learning of partial differential equations in modal space
- When and why PINNs fail to train: a neural tangent kernel perspective
- Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems
- Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
- A composite neural network that learns from multi-fidelity data: application to function approximation and inverse PDE problems
- On the eigenvector bias of Fourier feature networks: from regression to solving multi-scale PDEs with physics-informed neural networks
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Seamless integration of global Dirichlet-to-Neumann boundary condition and spectral elements for transformation electromagnetics
- Transfinite element methods: Blending-function interpolation over arbitrary curved element domains
- Convergence analysis for finite element discretizations of the Helmholtz equation with Dirichlet-to-Neumann boundary conditions
- Neural‐network‐based approximations for solving partial differential equations
- High-Order Methods for Incompressible Fluid Flow
- Functional Analysis for Helmholtz Equation in the Framework of Domain Decomposition
- Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations
- Deep Learning Architectures
- An Adaptive Perfectly Matched Layer Method for Multiple Cavity Scattering Problems
- Linear integral equations
- Acoustic and electromagnetic equations. Integral representations for harmonic problems
- Neural tangent kernel: convergence and generalization in neural networks (invited paper)
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