Image de couverture de livre

Adaptive quadratures for nonlinear approximation of low-dimensional PDEs using smooth neural networks

Fuente: arXiv

Enregistré dans:

Détails bibliographiques
Auteurs principaux:	Magueresse, Alexandre, Badia, Santiago
Format:	Preprint
Publié:	2023
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

A convergence framework for energy minimisation of linear self-adjoint elliptic PDEs in nonlinear approximation spaces
par: Magueresse, Alexandre, et autres
Publié: (2025)

Adaptive anisotropic composite quadratures for residual minimisation in neural PDE approximations
par: Badia, Santiago, et autres
Publié: (2026)

Energy minimisation using overlapping tensor-product free-knot B-splines
par: Magueresse, Alexandre, et autres
Publié: (2025)

Compatible finite element interpolated neural networks
par: Badia, Santiago, et autres
Publié: (2024)

Unfitted finite element interpolated neural networks
par: Li, Wei, et autres
Publié: (2025)

Functional tensor train neural network for solving high-dimensional PDEs
par: Feng, Yani, et autres
Publié: (2025)

Multilevel Picard approximations overcome the curse of dimensionality in the numerical approximation of general semilinear PDEs with gradient-dependent nonlinearities
par: Neufeld, Ariel, et autres
Publié: (2023)

Deep neural network approximation theory for high-dimensional functions
par: Beneventano, Pierfrancesco, et autres
Publié: (2021)

Four-field mixed finite elements for incompressible nonlinear elasticity
par: Badia, Santiago, et autres
Publié: (2026)

Accelerating the convergence of Newton's method for nonlinear elliptic PDEs using Fourier neural operators
par: Aghili, Joubine, et autres
Publié: (2024)

Multilevel quadrature formulae for the optimal control of random PDEs
par: Nobile, Fabio, et autres
Publié: (2024)

Adaptive Finite Element Interpolated Neural Networks
par: Badia, Santiago, et autres
Publié: (2024)

A Deep BSDE approximation of nonlinear integro-PDEs with unbounded nonlocal operators
par: Jakobsen, Espen Robstad, et autres
Publié: (2024)

Simpson's quadrature for a nonlinear variational symplectic scheme
par: Dubois, François, et autres
Publié: (2024)

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

High-dimensional approximation spaces of artificial neural networks and applications to partial differential equations
par: Beneventano, Pierfrancesco, et autres
Publié: (2020)

A posteriori certification for neural network approximations to PDEs
par: Ernst, Lewin, et autres
Publié: (2025)

General transformation neural networks: A class of parametrized functions for high-dimensional function approximation
par: Wang, Xiaoyang, et autres
Publié: (2025)

Gauss Newton method for solving variational problems of PDEs with neural network discretizaitons
par: Hao, Wenrui, et autres
Publié: (2023)

Adaptive neural network basis methods for partial differential equations with low-regular solutions
par: Huang, Jianguo, et autres
Publié: (2024)

A unified framework for multiscale spectral generalized FEMs and low-rank approximations to multiscale PDEs
par: Ma, Chupeng
Publié: (2023)

Inverse scattering beyond Born approximation via rotation-equivariance-aware neural network and low-rank structure
par: Zhou, Yuyuan, et autres
Publié: (2026)

A new variable shape parameter strategy for RBF approximation using neural networks
par: Mojarrad, Fatemeh Nassajian, et autres
Publié: (2022)

On understanding and overcoming spectral biases of deep neural network learning methods for solving PDEs
par: Xu, Zhi-Qin John, et autres
Publié: (2025)

STLCutters.jl: A scalable geometrical framework library for unfitted finite element discretisations
par: Martorell, Pere A., et autres
Publié: (2024)

An efficient stochastic particle method for high-dimensional nonlinear PDEs
par: Lei, Zhengyang, et autres
Publié: (2023)

On low-dimensional approximation of function spaces of interior regularity
par: Aziz, S., et autres
Publié: (2025)

Fredholm integral equations for function approximation and the training of neural networks
par: Gelß, Patrick, et autres
Publié: (2023)

A nonsmooth extension of the Brezzi-Rappaz-Raviart approximation theorem via metric regularity techniques and applications to nonlinear PDEs
par: Berry, Jules, et autres
Publié: (2025)

Space-time deep neural network approximations for high-dimensional partial differential equations
par: Hornung, Fabian, et autres
Publié: (2020)

A discrete trace theory for non-conforming polytopal hybrid discretisation methods
par: Badia, Santiago, et autres
Publié: (2024)

High-precision quadrature via local Fourier extension: analytic integration, uniform sampling, and correction for piecewise smooth integrands
par: Liu, Xinran, et autres
Publié: (2026)

Weak TransNet: A Petrov-Galerkin based neural network method for solving elliptic PDEs
par: Xu, Zhihang, et autres
Publié: (2025)

Combining physics-informed graph neural network and finite difference for solving forward and inverse spatiotemporal PDEs
par: Zhang, Hao, et autres
Publié: (2024)

Sharp uniform approximation for spectral Barron functions by deep neural networks
par: Liao, Yulei, et autres
Publié: (2025)

Error estimates of physics-informed neural networks for approximating Boltzmann equation
par: Abdo, Elie, et autres
Publié: (2024)

Rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of gradient-dependent semilinear heat equations
par: Neufeld, Ariel, et autres
Publié: (2024)

Deep ReLU neural networks overcome the curse of dimensionality when approximating semilinear partial integro-differential equations
par: Neufeld, Ariel, et autres
Publié: (2023)

HANN: Homotopy auxiliary neural network for solving nonlinear algebraic equations
par: Zai, Ling-Zhe, et autres
Publié: (2025)

Extended Galerkin neural network approximation of singular variational problems with error control
par: Ainsworth, Mark, et autres
Publié: (2024)