Cover Image

Variationally Correct Neural Residual Regression for Parametric PDEs: On the Viability of Controlled Accuracy

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Bachmayr, Markus, Dahmen, Wolfgang, Oster, Mathias
Format:	Preprint
Published:	2024
Subjects:	Numerical Analysis
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Preconditioning and Numerical Stability in Neural Network Training for Parametric PDEs
by: Bachmayr, Markus, et al.
Published: (2026)

An adaptive space-time method for nonlinear poroviscoelastic flows with discontinuous porosities
by: Bachmayr, Markus, et al.
Published: (2024)

A space-time adaptive low-rank method for high-dimensional parabolic partial differential equations
by: Bachmayr, Markus, et al.
Published: (2023)

Accuracy Controlled Schemes for the Eigenvalue Problem of the Radiative Transfer Equation
by: Dahmen, Wolfgang, et al.
Published: (2023)

Variationally correct operator learning: Reduced basis neural operator with a posteriori error estimation
by: Qiu, Yuan, et al.
Published: (2025)

Point Cloud Neural Operator for Parametric PDEs on Complex and Variable Geometries
by: Zeng, Chenyu, et al.
Published: (2025)

Sparse and low-rank approximations of parametric elliptic PDEs: the best of both worlds
by: Bachmayr, Markus, et al.
Published: (2025)

A comparison study of supervised learning techniques for the approximation of high dimensional functions and feedback control
by: Oster, Mathias, et al.
Published: (2024)

Hybrid Iterative Solvers with Geometry-Aware Neural Preconditioners for Parametric PDEs
by: Lee, Youngkyu, et al.
Published: (2025)

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

DPG loss functions for learning parameter-to-solution maps by neural networks
by: Castillo, Pablo Cortés, et al.
Published: (2025)

Multilevel CNNs for Parametric PDEs based on Adaptive Finite Elements
by: Schütte, Janina Enrica, et al.
Published: (2024)

Besov regularity of non-linear parabolic PDEs on non-convex polyhedral domains
by: Dahlke, Stephan, et al.
Published: (2021)

Numerical study of Galerkin-collocation approximation in time for the wave equation
by: Anselmann, Mathias, et al.
Published: (2019)

Expansive Natural Neural Gradient Flows for Energy Minimization
by: Dahmen, Wolfgang, et al.
Published: (2025)

Stochastic Quadrature Rules for Solving PDEs using Neural Networks
by: Taylor, Jamie M., et al.
Published: (2025)

Solving High-Dimensional PDEs Using Linearized Neural Networks
by: Mao, Tong, et al.
Published: (2026)

Stable Mesh-Free Variational Radial Basis Function Approximation for Elliptic PDEs and Obstacle Problems
by: Le, Tan Phuong Dong, et al.
Published: (2026)

Adaptive-Growth Randomized Neural Networks for PDEs: Algorithms and Numerical Analysis
by: Dang, Haoning, et al.
Published: (2024)

Nodal Hybrid Neural Solvers for Parametric PDE Systems
by: Liu, Yun, et al.
Published: (2025)

Reduced-Basis Deep Operator Learning for Parametric PDEs with Independently Varying Boundary and Source Data
by: Wang, Yueqi, et al.
Published: (2025)

Low-rank tensor product Richardson iteration for radiative transfer in plane-parallel geometry
by: Bachmayr, Markus, et al.
Published: (2024)

Low-rank eigenvalue solvers for block-sparse matrix product states
by: Bachmayr, Markus, et al.
Published: (2026)

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

PINNsur: Physics-Informed Neural Networks for PDEs on Curved Surfaces
by: Jain, Pranav, et al.
Published: (2026)

Neural Measures for learning distributions of Random PDEs
by: Arampatzis, Georgios, et al.
Published: (2025)

Neural Evolutionary Kernel Method: A Knowledge-Guided Framework for Solving Evolutionary PDEs
by: Ling, Shuo, et al.
Published: (2026)

What Can One Expect When Solving PDEs Using Shallow Neural Networks?
by: He, Roy Y., et al.
Published: (2025)

Predictive Moving Sample Method for Physics-Informed Neural Solvers of Time-Dependent PDEs
by: Xu, Beining, et al.
Published: (2026)

Bias and Multiscale Correction Methods for Variational State Estimation
by: Galarce, Felipe, et al.
Published: (2023)

Adaptive Multilevel Neural Networks for Parametric PDEs with Error Estimation
by: Schütte, Janina E., et al.
Published: (2024)

Convergence Guarantees for Gradient-Based Training of Neural PDE Solvers: From Linear to Nonlinear PDEs
by: Zhao, Wei, et al.
Published: (2025)

Variational Matrix-Learning Fourier Networks for Parametric Multiphysics Surrogates
by: Li, Xinyu, et al.
Published: (2026)

Dynamical low-rank tensor approximations to high-dimensional parabolic problems: existence and convergence of spatial discretizations
by: Bachmayr, Markus, et al.
Published: (2023)

Iterative thresholding low-rank time integration
by: Bachmayr, Markus, et al.
Published: (2025)

Galerkin Neural Network-POD for Acoustic and Electromagnetic Wave Propagation in Parametric Domains
by: Weder, Philipp, et al.
Published: (2024)

Leveraging Lie Group Symmetries to Enhance Physics-Informed Neural Networks for the Fundamental Solution of Linear PDEs
by: Jiao, Xiaopei, et al.
Published: (2024)

Latent Neural Operator Pretraining for Solving Time-Dependent PDEs
by: Wang, Tian, et al.
Published: (2024)

Learning quantities of interest from parametric PDEs: An efficient neural-weighted Minimal Residual approach
by: Brevis, Ignacio, et al.
Published: (2023)

Fourier Neural Operator with Learned Deformations for PDEs on General Geometries
by: Li, Zongyi, et al.
Published: (2022)