Cover Image

When can a neural operator replace a coarse solve? Architectural principles for two-level preconditioning

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Melchers, Hugo, Abdelmalik, Michael, Dolean, Victorita
Format:	Preprint
Published:	2026
Subjects:	Numerical Analysis 68T07 (Primary) 65F08, 65N55 (Secondary) I.2.6; G.1.3; G.1.8
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Numerical Solution of Mixed-Dimensional PDEs Using a Neural Preconditioner
by: Dimola, Nunzio, et al.
Published: (2025)

Challenges in automatic differentiation and numerical integration in physics-informed neural networks modelling
by: Daněk, Josef, et al.
Published: (2024)

Learning a generalized multiscale prolongation operator
by: Liu, Yucheng, et al.
Published: (2024)

Neural Green's Operators for Parametric Partial Differential Equations
by: Melchers, Hugo, et al.
Published: (2024)

Deceptron: Learned Local Inverses for Fast and Stable Physics Inversion
by: Kachhadiya, Aaditya L.
Published: (2025)

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

Learning Hamiltonian flows from numerical integrators and examples
by: Fang, Rui, et al.
Published: (2025)

On adaptive BDDC for the flow in heterogeneous porous media
by: Sousedík, Bedřich
Published: (2019)

Inexact and primal multilevel FETI-DP methods: a multilevel extension and interplay with BDDC
by: Sousedík, Bedřich
Published: (2022)

Sprecher Networks: A Parameter-Efficient Kolmogorov-Arnold Architecture
by: Hägg, Christian, et al.
Published: (2025)

On the Convergence Behavior of Preconditioned Gradient Descent Toward the Rich Learning Regime
by: Jiang, Shuai, et al.
Published: (2026)

Alternately-optimized SNN method for acoustic scattering problem in unbounded domain
by: Song, Haoming, et al.
Published: (2025)

RANDSMAPs: Random-Feature/multi-Scale Neural Decoders with Mass Preservation
by: Patsatzis, Dimitrios G., et al.
Published: (2026)

A Classical-Quantum Hybrid Architecture for Physics-Informed Neural Networks
by: Lantigua, Said, et al.
Published: (2025)

On the study of frequency control and spectral bias in Wavelet-Based Kolmogorov Arnold networks: A path to physics-informed KANs
by: Meshir, Juan Daniel, et al.
Published: (2025)

Balancing Inexactness in Mixed Precision Matrix Computations
by: Carson, Erin Claire
Published: (2026)

Discontinuous Galerkin finite element operator network for solving non-smooth PDEs
by: Chawla, Kapil, et al.
Published: (2026)

Latent Twins
by: Chung, Matthias, et al.
Published: (2025)

Data-induced multiscale losses and efficient multirate gradient descent schemes
by: He, Juncai, et al.
Published: (2024)

Neural Approximate Inverse Preconditioners
by: Xu, Tianshi, et al.
Published: (2025)

Comparing EPGP Surrogates and Finite Elements Under Degree-of-Freedom Parity
by: Amo, Obed, et al.
Published: (2025)

Inexact Gauss Seidel and Coarse Solvers for AMG and s-step CG
by: Thomas, Stephen, et al.
Published: (2025)

Local properties of neural networks through the lens of layer-wise Hessians
by: Bolshim, Maxim, et al.
Published: (2025)

Inter-Layer Hessian Analysis of Neural Networks with DAG Architectures
by: Bolshim, Maxim, et al.
Published: (2026)

Total Generalized Variation regularization closes the gap between neural-eld and classical methods in seismic travel-time tomography
by: Kurosawa, Isao
Published: (2026)

Kourkoutas-Beta: A Sunspike-Driven Adam Optimizer with Desert Flair
by: Kassinos, Stavros C.
Published: (2025)

Stabilized Adaptive Loss and Residual-Based Collocation for Physics-Informed Neural Networks
by: Singh, Divyavardhan, et al.
Published: (2026)

Can Symmetric Positive Definite (SPD) coarse spaces perform well for indefinite Helmholtz problems?
by: Dolean, Victorita, et al.
Published: (2024)

MgFNO: Multi-grid Architecture Fourier Neural Operator for Parametric Partial Differential Equations
by: Guo, Zi-Hao, et al.
Published: (2024)

STM Image Analysis using Autoencoders
by: Binev, Peter, et al.
Published: (2025)

Frequency Bias and OOD Generalization in Neural Operators under a Variable-Coefficient Wave Equation
by: Xie, Runlong, et al.
Published: (2026)

Data-driven linear solver selection and performance tuning for multiphysics simulations in porous media
by: Zabegaev, Yury, et al.
Published: (2025)

Parametric Numerical Integration with (Differential) Machine Learning
by: Leitao, Álvaro, et al.
Published: (2025)

Space-time parallel scaling of Parareal with a physics-informed Fourier Neural Operator coarse propagator applied to the Black-Scholes equation
by: Ibrahim, Abdul Qadir, et al.
Published: (2024)

Learning Nonlinear Finite Element Solution Operators using Multilayer Perceptrons and Energy Minimization
by: Larson, Mats G., et al.
Published: (2024)

Learning Chaotic Dynamics through Second-Order Geometric Supervision
by: Kang, Shinhoo, et al.
Published: (2026)

Concepts for Composing Finite Element Function Space Bases
by: Engwer, Christian, et al.
Published: (2025)

The Evolution of Computer-Assisted Proof In Analysis
by: Rychlik, Marek
Published: (2026)

HODLR$d$D: A new Black-box fast algorithm for $N$-body problems in $d$-dimensions with guaranteed error bounds
by: Khan, Ritesh, et al.
Published: (2022)

Towards Model Discovery Using Domain Decomposition and PINNs
by: Saha, Tirtho S., et al.
Published: (2024)