Cover Image

Robust PDE discovery under sparse and highly noisy conditions via attention neural networks

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Zhang, Shilin, Huang, Yunqing, Yi, Nianyu, Zhang, shihan
Format:	Preprint
Published:	2025
Subjects:	Numerical Analysis
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

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

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

DataTransfer: Neural network based interpolation across non-nested meshes
by: Hao, Jiaxiong, et al.
Published: (2025)

Rank Inspired Neural Network for solving linear partial differential equations
by: Peng, Wentao, et al.
Published: (2025)

Weights initialization of neural networks for function approximation
by: Hu, Xinwen, et al.
Published: (2025)

A posteriori error estimators for fourth order elliptic problems with concentrated loads
by: Cao, Huihui, et al.
Published: (2024)

Transcending Sparse Measurement Limits: Operator-Learning-Driven Data Super-Resolution for Inverse Source Problem
by: Pan, Guanyu, et al.
Published: (2025)

Neural network-enhanced $hr$-adaptive finite element algorithm for parabolic equations
by: Hao, Jiaxiong, et al.
Published: (2025)

Towards $C^0$ finite element methods for fourth-order elliptic equation. Part I: general boundary conditions
by: Zhang, Xihao, et al.
Published: (2026)

A linear, unconditionally stable, second order decoupled method for the Ericksen-Leslie model with SAV approach
by: Cao, Ruonan, et al.
Published: (2025)

Inverse source problems for the stochastic wave equations
by: Huang, Yunqing, et al.
Published: (2025)

High Accuracy Techniques Based Adaptive Finite Element Methods for Elliptic PDEs
by: Xiao, Jingjing, et al.
Published: (2025)

Learning smooth functions in high dimensions: from sparse polynomials to deep neural networks
by: Adcock, Ben, et al.
Published: (2024)

Multi-stage PDE-based image processing techniques for noisy MRI scans
by: Slepova, Ksenia, et al.
Published: (2025)

Robust space-time multiscale upscaling via multicontinuum homogenization for evolving perforated media
by: Xie, Wei, et al.
Published: (2025)

Tensor neural networks for high-dimensional Fokker-Planck equations
by: Wang, Taorui, et al.
Published: (2024)

Enhanced gradient recovery-based a posteriori error estimator and adaptive finite element method for elliptic equations
by: Liu, Ying, et al.
Published: (2025)

Unconditionally energy stable IEQ-FEMs for the Cahn-Hilliard equation and Allen-Cahn equation
by: Chen, Yaoyao, et al.
Published: (2024)

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

Inf-Sup neural networks for high-dimensional elliptic PDE problems
by: Huo, Xiaokai, et al.
Published: (2024)

A hierarchical approach for multicontinuum homogenization in high contrast media
by: Xie, Wei, et al.
Published: (2025)

Solving forward and inverse PDE problems on unknown manifolds via physics-informed neural operators
by: Jiao, Anran, et al.
Published: (2024)

Deep neural network approximation theory for high-dimensional functions
by: Beneventano, Pierfrancesco, et al.
Published: (2021)

Data-driven discovery of chemical reaction networks
by: Reyes-Velazquez, Abraham, et al.
Published: (2026)

Adaptive anisotropic composite quadratures for residual minimisation in neural PDE approximations
by: Badia, Santiago, et al.
Published: (2026)

A virtual element method with IMEX-SAV scheme for the incompressible magnetohydrodynamics equations
by: Dong, Xiaojing, et al.
Published: (2024)

Conservative nonconforming virtual element method for stationary incompressible magnetohydrodynamics
by: Dong, Xiaojing, et al.
Published: (2024)

Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features
by: Li, Ke, et al.
Published: (2024)

Two-scale neural networks for optimal control of linear convection-dominated equations
by: Liu, Sijing, et al.
Published: (2026)

An adaptive time-stepping strategy for the modified phase field crystal model with a strong nonlinear vacancy potential
by: Hao, Wanrong, et al.
Published: (2025)

Deep neural network approximation for high-dimensional parabolic partial integro-differential equations
by: Baranek, Marcin
Published: (2025)

Superconvergent quadriatic finite element on uniform tetrahedral meshes
by: Huang, Yunqing, et al.
Published: (2025)

Inverse source problem for the parabolic equation with sparse moving observations
by: Gu, Qiling, et al.
Published: (2026)

Determine the point source of the heat equation with sparse boundary measurements
by: Gu, Qiling, et al.
Published: (2025)

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

General transformation neural networks: A class of parametrized functions for high-dimensional function approximation
by: Wang, Xiaoyang, et al.
Published: (2025)

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

Estimation of sparse polynomial approximation error to continuous function
by: Feng, Renzhong, et al.
Published: (2025)

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions
by: Zhang, Yaqin, et al.
Published: (2025)

A residual driven multiscale method for Darcy's flow in perforated domains
by: Xie, Wei, et al.
Published: (2025)