arXiv Machine Learning June 2, 2026 By Seungchan Ko, Jiyeon Kim, Dongwook Shin

Sparse FEONet: A Low-Cost, Memory-Efficient Operator Network via Finite-Element Local Sparsity for Parametric PDEs

Read the original on arXiv Machine Learning →

arXiv:2601. 00672v2 Announce Type: replace-cross Abstract: In this paper, we study the finite element operator network (FEONet), an operator-learning method for parametric problems, originally introduced in J.

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arXiv Machine Learning

4d ago

Learning Nonlinear Finite Element Solution Operators using Multilayer Perceptrons and Energy Minimization

arXiv:2412.04596v3 Announce Type: replace Abstract: We develop and evaluate a method for learning solution operators to nonlinear problems governed by partial differential equations (PDEs). The appro...

By Mats G. Larson, Carl Lundholm, Anna Persson

arXiv Machine Learning

Aug 3

RAPNet: Accelerating Algebraic Multigrid with Learned Sparse Corrections

arXiv:2605. 26854v2 Announce Type: replace Abstract: The scalable solution of large sparse linear systems is a bottleneck in scientific computing and graph analysis.

By Yali Fink, Ido Ben-Yair, Lars Ruthotto, Eran Treister

efficiency

arXiv Machine Learning

Jul 31

Learning the Helmholtz equation operator with DeepONet for non-parametric 2D geometries

arXiv:2605. 00760v2 Announce Type: replace Abstract: This paper deals with solving the 2D Helmholtz equation on non-parametric domains, leveraging a physics-informed neural operator network, the DeepONet framework.

By Rodolphe Barlogis, Ferhat Tamssaouet, Quentin Falcoz, St\'ephane Grieu

arXiv Machine Learning

Jun 9

Mesh Graph Neural Network Framework for Accelerating Finite Element Simulation for Arbitrary Geometries

arXiv:2606. 08287v1 Announce Type: new Abstract: Finite element analysis (FEA) is essential for structural design but remains computationally expensive, particularly when evaluating multiple design iterations or load scenarios.

By Josiah D. Kunz, Kamal Choudhary

arXiv Machine Learning

Jun 5

Learning solution operators of PDEs with sparse approximation methods

arXiv:2606. 06046v1 Announce Type: cross Abstract: We investigate the approximation of solution operators for partial differential equations (PDEs) using sparse high-dimensional techniques.

By Sebastian Neumayer, Daniel Potts, Fabian Taubert

arXiv Machine Learning

Jul 31

Graph Neural Multilevel Preconditioners for Iterative Solvers

arXiv:2607. 28456v1 Announce Type: cross Abstract: Solving large, sparse linear systems is a core task in scientific computing, and efficient iterative solvers rely critically on effective and robust preconditioning.

By Zechen Zhang, Rui Peng Li, Yousef Saad

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Learning Nonlinear Finite Element Solution Operators using Multilayer Perceptrons and Energy Minimization

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