mlsanityData to 7 Oct 2026

Multiscale Neural Operators for Solving Time-Independent PDEs

arXiv 2311.05964 ↗First posted 10 Nov 2023cs.LGcited by 5

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Abstract (arXiv)

Time-independent Partial Differential Equations (PDEs) on large meshes pose significant challenges for data-driven neural PDE solvers. We introduce a novel graph rewiring technique to tackle some of these challenges, such as aggregating information across scales and on irregular meshes. Our proposed approach bridges distant nodes, enhancing the global interaction capabilities of GNNs. Our experiments on three datasets reveal that GNN-based methods set new performance standards for time-independent PDEs on irregular meshes. Finally, we show that our graph rewiring strategy boosts the performance of baseline methods, achieving state-of-the-art results in one of the tasks.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 22 of its 26 references that are in the map. First posted on arXiv 10 Nov 2023.

Builds on

22 of 26 references.

References · 22

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10 more
  1. 2020Multipole Graph Neural Operator for Parametric Partial Differential Equationscited by 343
  2. 2022Transformer for Partial Differential Equations' Operator Learningcited by 270
  3. 2022Long Range Graph Benchmarkcited by 258
  4. 2020Model Reduction and Neural Networks for Parametric PDEscited by 257
  5. 2022Towards Multi-spatiotemporal-scale Generalized PDE Modelingcited by 190
  6. 2023DRew: Dynamically Rewired Message Passing with Delaycited by 81
  7. 2022Learning the Solution Operator of Boundary Value Problems using Graph Neural Networkscited by 17
  8. 2022Towards Fast Simulation of Environmental Fluid Mechanics with Multi-Scale Graph Neural Networkscited by 11
  9. 2023GNN-based physics solver for time-independent PDEscited by 10
  10. 2023Enhancing Multi-Objective Optimization through Machine Learning-Supported Multiphysics Simulationcited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 1; 2026: 2.

5 papers.

  1. 2024From Structured to Unstructured:A Comparative Analysis of Computer Vision and Graph Models in solving Mesh-based PDEscited by 1
  2. 2024ConDiff: A Challenging Dataset for Neural Solvers of Partial Differential Equationscited by 0
  3. 2025PIBNet: a Physics-Inspired Boundary Network for Multiple Scattering Simulationscited by 0
  4. 2026Read, Write, Relax: Why Neural PDE Surrogates Need Both Global and Local Processingcited by 0
  5. 2026ScaGNN: a Graph Neural Network for Multiple Scattering Simulationscited by 0