Cover Image

Gauss Newton method for solving variational problems of PDEs with neural network discretizaitons

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Hao, Wenrui, Hong, Qingguo, Jin, Xianlin
Format:	Preprint
Published:	2023
Subjects:	Numerical Analysis
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

On understanding and overcoming spectral biases of deep neural network learning methods for solving PDEs
by: Xu, Zhi-Qin John, et al.
Published: (2025)

Functional tensor train neural network for solving high-dimensional PDEs
by: Feng, Yani, et al.
Published: (2025)

Weak TransNet: A Petrov-Galerkin based neural network method for solving elliptic PDEs
by: Xu, Zhihang, et al.
Published: (2025)

The discrete inverse conductivity problem solved by the weights of an interpretable neural network
by: Beretta, Elena, et al.
Published: (2024)

Combining physics-informed graph neural network and finite difference for solving forward and inverse spatiotemporal PDEs
by: Zhang, Hao, et al.
Published: (2024)

Accelerating the convergence of Newton's method for nonlinear elliptic PDEs using Fourier neural operators
by: Aghili, Joubine, et al.
Published: (2024)

HomPINNs: homotopy physics-informed neural networks for solving the inverse problems of nonlinear differential equations with multiple solutions
by: Zheng, Haoyang, et al.
Published: (2023)

Domain decomposition architectures and Gauss-Newton training for physics-informed neural networks
by: Heinlein, Alexander, et al.
Published: (2025)

An inexact Matrix-Newton method for solving NEPv
by: Werner, Tom
Published: (2023)

Subspace method based on neural networks for solving the partial differential equation
by: Xu, Zhaodong, et al.
Published: (2024)

Deep collocation method: A framework for solving PDEs using neural networks with error control
by: Weng, Mingxing, et al.
Published: (2025)

A piecewise neural network method for solving large interval solution to initial value problem of ordinary differential equations
by: Han, Dongpeng, et al.
Published: (2024)

A correction adaptive two-grid finite element method for nonselfadjoint or indefinite elliptic problems
by: Li, Fei, et al.
Published: (2026)

Improved randomized neural network methods with boundary processing for solving elliptic equations
by: Zhou, Huifang, et al.
Published: (2024)

Physics-informed neural networks for solving two-phase flow problems with moving interfaces
by: Zhai, Qijia, et al.
Published: (2026)

Subspace method based on neural networks for solving the partial differential equation in weak form
by: Liu, Pengyuan, et al.
Published: (2024)

VS-PINN: A fast and efficient training of physics-informed neural networks using variable-scaling methods for solving PDEs with stiff behavior
by: Ko, Seungchan, et al.
Published: (2024)

IG-PINNs: Interface-gated physics-informed neural networks for solving elliptic interface problems
by: Zheng, Jiachun, et al.
Published: (2025)

Extended Galerkin neural network approximation of singular variational problems with error control
by: Ainsworth, Mark, et al.
Published: (2024)

An extended Gauss-Newton method for full waveform inversion
by: Gholami, Ali
Published: (2023)

Spectral integrated neural networks (SINNs) for solving forward and inverse dynamic problems
by: Qiu, Lin, et al.
Published: (2024)

Pseudospectral method for solving PDEs using Matrix Product States
by: Gidi, Jorge, et al.
Published: (2024)

Error analysis for finite element operator learning methods for solving parametric second-order elliptic PDEs
by: Hong, Youngjoon, et al.
Published: (2024)

A neural operator framework for solving inverse scattering problems
by: Chenu, Victor, et al.
Published: (2026)

Data-integrated neural networks for solving partial differential equations
by: Zheng, Jiachun, et al.
Published: (2025)

A Primal-dual hybrid gradient method for solving optimal control problems and the corresponding Hamilton-Jacobi PDEs
by: Meng, Tingwei, et al.
Published: (2024)

Asymptotic quadratic convergence of the Gauss-Newton method for complex phase retrieval
by: Huang, Meng
Published: (2024)

Newton Informed Neural Operator for Computing Multiple Solutions of Nonlinear Partials Differential Equations
by: Hao, Wenrui, et al.
Published: (2024)

A simple-to-implement nonlinear preconditioning of Newton's method for solving the steady Navier-Stokes equations
by: Mohebujjaman, Muhammad, et al.
Published: (2025)

Deep Energy Method with Large Language Model assistance: an open-source Streamlit-based platform for solving variational PDEs
by: Wang, Yizheng, et al.
Published: (2026)

HANN: Homotopy auxiliary neural network for solving nonlinear algebraic equations
by: Zai, Ling-Zhe, et al.
Published: (2025)

On pattern formation in the thermodynamically-consistent variational Gray-Scott model
by: Hao, Wenrui, et al.
Published: (2024)

Optimal error estimates of the diffuse domain method for parabolic equations
by: Hao, Wenrui, et al.
Published: (2025)

Multigrid method for nonlinear eigenvalue problems based on Newton iteration
by: Xu, Fei, et al.
Published: (2024)

Shallow neural network yields regularization for ill-posed inverse problems
by: Wang, Lan, et al.
Published: (2025)

Adaptive quadratures for nonlinear approximation of low-dimensional PDEs using smooth neural networks
by: Magueresse, Alexandre, et al.
Published: (2023)

A preconditioned iteration method for solving saddle point problems
by: Zhang, Juan, et al.
Published: (2024)

A fast neural hybrid Newton solver adapted to implicit methods for nonlinear dynamics
by: Jin, Tianyu, et al.
Published: (2024)

Inexact Gauss-Newton methods with matrix approximation by sampling for nonlinear least-squares and systems
by: Bellavia, Stefania, et al.
Published: (2023)

Geometric local parameterization for solving Hele-Shaw problems with surface tension
by: Zhang, Zengyan, et al.
Published: (2025)