Cover Image

Convergence Guarantees for Gradient-Based Training of Neural PDE Solvers: From Linear to Nonlinear PDEs

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Zhao, Wei, Luo, Tao
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

Learning Neural PDE Solvers with Convergence Guarantees
by: Hsieh, Jun-Ting, et al.
Published: (2019)

Quantifying Training Difficulty and Accelerating Convergence in Neural Network-Based PDE Solvers
by: Chen, Chuqi, et al.
Published: (2024)

Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation
by: Zhang, Rui, et al.
Published: (2023)

Supervised and Unsupervised Neural Network Solver for First Order Hyperbolic Nonlinear PDEs
by: Baba, Zakaria, et al.
Published: (2026)

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

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

UGrid: An Efficient-And-Rigorous Neural Multigrid Solver for Linear PDEs
by: Han, Xi, et al.
Published: (2024)

Deep Picard Iteration for High-Dimensional Nonlinear PDEs
by: Han, Jiequn, et al.
Published: (2024)

Physics-Informed Gaussian Process Regression Generalizes Linear PDE Solvers
by: Pförtner, Marvin, et al.
Published: (2022)

Blending Neural Operators and Relaxation Methods in PDE Numerical Solvers
by: Zhang, Enrui, et al.
Published: (2022)

Unisolver: PDE-Conditional Transformers Towards Universal Neural PDE Solvers
by: Zhou, Hang, et al.
Published: (2024)

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

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

Are Deep Learning Based Hybrid PDE Solvers Reliable? Why Training Paradigms and Update Strategies Matter
by: Wu, Yuhan, et al.
Published: (2026)

Transolver: A Fast Transformer Solver for PDEs on General Geometries
by: Wu, Haixu, et al.
Published: (2024)

Convergence Analysis of An Alternating Nonlinear GMRES on Linear Systems
by: He, Yunhui
Published: (2025)

DDC-PINNs: A Predictor-Corrector Approach Based on Neural Network-Driven Domain Decomposition and Classical ODE Solvers for Time-Dependent PDEs
by: Yang, Xun, et al.
Published: (2025)

SlabLU: A Two-Level Sparse Direct Solver for Elliptic PDEs
by: Yesypenko, Anna, et al.
Published: (2022)

Convergence and error control of consistent PINNs for elliptic PDEs
by: Bonito, Andrea, et al.
Published: (2024)

Learning from Linear Algebra: A Graph Neural Network Approach to Preconditioner Design for Conjugate Gradient Solvers
by: Trifonov, Vladislav, et al.
Published: (2024)

Better Neural PDE Solvers Through Data-Free Mesh Movers
by: Hu, Peiyan, et al.
Published: (2023)

Spline-Based Stochastic Collocation Methods for Uncertainty Quantification in Nonlinear Hyperbolic PDEs
by: Chertock, Alina, et al.
Published: (2024)

A Fast Direct Solver for Elliptic PDEs on a Hierarchy of Adaptively Refined Quadtrees
by: Chipman, Damyn, et al.
Published: (2024)

Deep Learning-Enhanced Preconditioning for Efficient Conjugate Gradient Solvers in Large-Scale PDE Systems
by: Li, Rui, et al.
Published: (2024)

Guaranteed stability bounds for second-order PDE problems satisfying a Garding inequality
by: Chaumont-Frelet, T.
Published: (2026)

Enhanced BPINN Training Convergence in Solving General and Multi-scale Elliptic PDEs with Noise
by: Hou, Yilong, et al.
Published: (2024)

Convergence of Physics-Informed Neural Networks for Fully Nonlinear PDE's
by: Arakelyan, Avetik, et al.
Published: (2024)

A Variational Framework for Residual-Based Adaptivity in Neural PDE Solvers and Operator Learning
by: Toscano, Juan Diego, et al.
Published: (2025)

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

Linearly implicit exponential integrators for damped Hamiltonian PDEs
by: Uzunca, Murat, et al.
Published: (2023)

A Stochastic Algorithm for Searching Saddle Points with Convergence Guarantee
by: Shi, Baoming, et al.
Published: (2025)

NonlinearSolve.jl: High-Performance and Robust Solvers for Systems of Nonlinear Equations in Julia
by: Pal, Avik, et al.
Published: (2024)

Adaptive Residual-Driven Newton Solver for Nonlinear Systems of Equations
by: Ding, Renjie, et al.
Published: (2025)

ALM-PINNs Algorithms for Solving Nonlinear PDEs and Parameter Inversion Problems
by: Tian, Yimeng, et al.
Published: (2024)

Solving Roughly Forced Nonlinear PDEs via Misspecified Kernel Methods and Neural Networks
by: Baptista, Ricardo, et al.
Published: (2025)

SSBE-PINN: A Sobolev Boundary Scheme Boosting Stability and Accuracy in Elliptic/Parabolic PDE Learning
by: Zhou, Qixuan, et al.
Published: (2025)

Learning Sparse Approximate Inverse Preconditioners for Conjugate Gradient Solvers on GPUs
by: Yang, Zherui, et al.
Published: (2025)

PDE Solvers Should Be Local: Fast, Stable Rollouts with Learned Local Stencils
by: Cheng, Chun-Wun, et al.
Published: (2025)

Flexible and Efficient Probabilistic PDE Solvers through Gaussian Markov Random Fields
by: Weiland, Tim, et al.
Published: (2025)

Differentiating Through Linear Solvers
by: Hovland, Paul, et al.
Published: (2024)