Image de couverture de livre

What Can One Expect When Solving PDEs Using Shallow Neural Networks?

Fuente: arXiv

Enregistré dans:

Détails bibliographiques
Auteurs principaux:	He, Roy Y., Liang, Ying, Zhao, Hongkai, Zhong, Yimin
Format:	Preprint
Publié:	2025
Sujets:	Numerical Analysis
Accès en ligne:	Acceder al recurso
Tags:	Ajouter un tag Pas de tags, Soyez le premier à ajouter un tag!

Documents similaires

From Frequency Bias to Spectral Balance: Operator-Aware Preconditioners for PINNs
par: He, Roy Y., et autres
Publié: (2026)

Why Shallow Networks Struggle to Approximate and Learn High Frequencies
par: Zhang, Shijun, et autres
Publié: (2023)

Solving High-Dimensional PDEs Using Linearized Neural Networks
par: Mao, Tong, et autres
Publié: (2026)

Structured and Balanced Multi-Component and Multi-Layer Neural Networks
par: Zhang, Shijun, et autres
Publié: (2024)

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs
par: De Ryck, T., et autres
Publié: (2025)

Stochastic Quadrature Rules for Solving PDEs using Neural Networks
par: Taylor, Jamie M., et autres
Publié: (2025)

Neural Evolutionary Kernel Method: A Knowledge-Guided Framework for Solving Evolutionary PDEs
par: Ling, Shuo, et autres
Publié: (2026)

WG-IDENT: Weak Group Identification of PDEs with Varying Coefficients
par: Tang, Cheng, et autres
Publié: (2025)

TINNs: Time-Induced Neural Networks for Solving Time-Dependent PDEs
par: Dai, Chen-Yang, et autres
Publié: (2026)

Phase-IDENT: Identification of Two-phase PDEs with Uncertainty Quantification
par: Yang, Edward L., et autres
Publié: (2026)

Solving PDEs on Spheres with Physics-Informed Convolutional Neural Networks
par: Lei, Guanhang, et autres
Publié: (2023)

Solving Roughly Forced Nonlinear PDEs via Misspecified Kernel Methods and Neural Networks
par: Baptista, Ricardo, et autres
Publié: (2025)

Solving PDEs on Unknown Manifolds with Machine Learning
par: Liang, Senwei, et autres
Publié: (2021)

Latent Neural Operator Pretraining for Solving Time-Dependent PDEs
par: Wang, Tian, et autres
Publié: (2024)

Solving Partial Differential Equations Using Artificial Neural Networks
par: Uriarte, Carlos
Publié: (2024)

Solving Nonlinear PDEs with Sparse Radial Basis Function Networks
par: Shao, Zihan, et autres
Publié: (2025)

Finite Element Eigenfunction Network (FEENet): A Hybrid Framework for Solving PDEs on Complex Geometries
par: Li, Shiyuan, et autres
Publié: (2026)

Incorporating Local Hölder Regularity into PINNs for Solving Elliptic PDEs
par: Zhou, Qirui, et autres
Publié: (2025)

FastLSQ: Solving PDEs in One Shot via Fourier Features with Exact Analytical Derivatives
par: Sulc, Antonin
Publié: (2026)

A Unified Weighted-Loss Physics-Informed Neural Network for Boundary Layer Problems in Singularly Perturbed PDEs
par: Hu, Wei-Fan, et autres
Publié: (2026)

Neural Multiscale Decomposition for Solving The Nonlinear Klein-Gordon Equation with Time Oscillation
par: Liang, Zhangyong, et autres
Publié: (2025)

Adaptive-Growth Randomized Neural Networks for PDEs: Algorithms and Numerical Analysis
par: Dang, Haoning, et autres
Publié: (2024)

ALM-PINNs Algorithms for Solving Nonlinear PDEs and Parameter Inversion Problems
par: Tian, Yimeng, et autres
Publié: (2024)

Convergence Analysis of Block Newton Methods for 1D Shallow Neural Network Approximation
par: Cai, Zhiqiang, et autres
Publié: (2026)

Finite Element Neural Network Interpolation. Part I: Interpretable and Adaptive Discretization for Solving PDEs
par: Škardová, Kateřina, et autres
Publié: (2024)

A Quantum Spectral Framework for Solving PDEs
par: Huang, Chih-Kang, et autres
Publié: (2026)

PINNsur: Physics-Informed Neural Networks for PDEs on Curved Surfaces
par: Jain, Pranav, et autres
Publié: (2026)

Generalization Error Analysis of Deep Backward Dynamic Programming for Solving Nonlinear PDEs
par: Ouyang, Du, et autres
Publié: (2024)

Finite Samples for Shallow Neural Networks
par: Xia, Yu, et autres
Publié: (2025)

Solving PDEs With Deep Neural Nets under General Boundary Conditions
par: Zhang, Chenggong
Publié: (2025)

Generalized Moving Least-Squares Methods for Solving Vector-valued PDEs on Unknown Manifolds
par: Li, Rongji, et autres
Publié: (2024)

A Meshfree RBF-FD Constant along Normal Method for Solving PDEs on Surfaces
par: Bayona, Víctor, et autres
Publié: (2024)

Convergence Guarantees for Gradient-Based Training of Neural PDE Solvers: From Linear to Nonlinear PDEs
par: Zhao, Wei, et autres
Publié: (2025)

Predictive Moving Sample Method for Physics-Informed Neural Solvers of Time-Dependent PDEs
par: Xu, Beining, et autres
Publié: (2026)

Posterior Concentration of Bayesian Physics-Informed Neural Networks for Elliptic PDEs
par: Zhao, Yuxuan, et autres
Publié: (2026)

RUNNs: Ritz-Uzawa Neural Networks for Solving Variational Problems
par: Herrera, Pablo, et autres
Publié: (2026)

Can Neural Networks learn Finite Elements?
par: Novo, Julia, et autres
Publié: (2024)

Leveraging Lie Group Symmetries to Enhance Physics-Informed Neural Networks for the Fundamental Solution of Linear PDEs
par: Jiao, Xiaopei, et autres
Publié: (2024)

Solving Inverse Acoustic Obstacle Scattering Problem with Phaseless Far-Field Measurement Using Deep Neural Network Surrogates
par: Fan, Yuxin, et autres
Publié: (2025)

Orthogonal Constrained Neural Networks for Solving Structured Inverse Eigenvalue Problems
par: Zhang, Shuai, et autres
Publié: (2024)