mlsanityData to 7 Oct 2026

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries

arXiv 2411.15178 ↗First posted 18 Nov 2024cs.LG cs.AIcited by 15

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Abstract (arXiv)

Partial Differential Equations (PDEs) underpin many scientific phenomena, yet traditional computational approaches often struggle with complex, nonlinear systems and irregular geometries. This paper introduces the AMG method, a Multi-Graph neural operator approach designed for efficiently solving PDEs on Arbitrary geometries. AMG leverages advanced graph-based techniques and dynamic attention mechanisms within a novel GraphFormer architecture, enabling precise management of diverse spatial domains and complex data interdependencies. By constructing multi-scale graphs to handle variable feature frequencies and a physics graph to encapsulate inherent physical properties, AMG significantly outperforms previous methods, which are typically limited to uniform grids. We present a comprehensive evaluation of AMG across six benchmarks, demonstrating its consistent superiority over existing state-of-the-art models. Our findings highlight the transformative potential of tailored graph neural operators in surmounting the challenges faced by conventional PDE solvers. Our code and datasets are available on https://github.com/lizhihao2022/AMG.

Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). Builds on 25 of its 45 references that are in the map. First posted on arXiv 18 Nov 2024.

Builds on

25 of 45 references.

References · 25

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13 more
  1. 2017Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphscited by 307
  2. 2024Transolver: A Fast Transformer Solver for PDEs on General Geometriescited by 299
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 6; 2026: 9.

15 papers.

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  1. 2025Towards Efficient Training of Graph Neural Networks: A Multiscale Approachcited by 4
  2. 2025LaDEEP: A Deep Learning-based Surrogate Model for Large Deformation of Elastic-Plastic Solidscited by 3
  3. 2025GFocal: A Global-Focal Neural Operator for Solving PDEs on Arbitrary Geometriescited by 2
  4. 2025Geometric Laplace Neural Operatorcited by 2
  5. 2026From Basis to Basis: Gaussian Particle Representation for Interpretable PDE Operatorscited by 2
  6. 2026DGNet: Discrete Green Networks for Data-Efficient Learning of Spatiotemporal PDEscited by 1
  7. 2025Reformulating Neural Operators in d+1 Dimensions for Embedding Evolutioncited by 0
  8. 2025MNO: Multiscale Neural Operator for 3D Computational Fluid Dynamicscited by 0
  9. 2026HGATSolver: A Heterogeneous Graph Attention Solver for Fluid-Structure Interactioncited by 0
  10. 2026SurgFormer: Scalable Learning of Organ Deformation with Resection Support and Real-Time Inferencecited by 0
  11. 2026MAVEN: A Mesh-Aware Volumetric Encoding Network for Simulating 3D Flexible Deformationcited by 0
  12. 2026NPSolver: Neural Poisson Solver with Iterative Physics Supervisioncited by 0
3 more
  1. 2026Factorized Neural Operators Decompose Dynamic and Persistent Responsescited by 0
  2. 2026From Fixed Grids to Moving Particles:A Transferable Latent Operator for Fluid Dynamicscited by 0
  3. 2026Joint Spatiotemporal Spectral Neural Operators for Learning PDEs on Irregular Domainscited by 0