mlsanityData to 7 Oct 2026

A Finite Element-Inspired Hypergraph Neural Network: Application to Fluid Dynamics Simulations

arXiv 2212.14545 ↗First posted 30 Dec 2022physics.flu-dyn cs.LGcited by 14

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Abstract (arXiv)

An emerging trend in deep learning research focuses on the applications of graph neural networks (GNNs) for mesh-based continuum mechanics simulations. Most of these learning frameworks operate on graphs wherein each edge connects two nodes. Inspired by the data connectivity in the finite element method, we present a method to construct a hypergraph by connecting the nodes by elements rather than edges. A hypergraph message-passing network is defined on such a node-element hypergraph that mimics the calculation process of local stiffness matrices. We term this method a finite element-inspired hypergraph neural network, in short FEIH(φ)-GNN. We further equip the proposed network with rotation equivariance, and explore its capability for modeling unsteady fluid flow systems. The effectiveness of the network is demonstrated on two common benchmark problems, namely the fluid flow around a circular cylinder and airfoil configurations. Stabilized and accurate temporal roll-out predictions can be obtained using the φ-GNN framework within the interpolation Reynolds number range. The network is also able to extrapolate moderately towards higher Reynolds number domain out of the training range.

Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). Builds on 26 of its 54 references that are in the map. First posted on arXiv 30 Dec 2022.

Builds on

26 of 54 references.

References · 26

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14 more
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Citing papers per year: 2024: 6; 2025: 4; 2026: 4.

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  1. 2024A review of graph neural network applications in mechanics-related domainscited by 14
  2. 2024Mesh-based Super-Resolution of Fluid Flows with Multiscale Graph Neural Networkscited by 10
  3. 2024H-SIREN: Improving implicit neural representations with hyperbolic periodic functionscited by 5
  4. 2024Continual Learning of Range-Dependent Transmission Loss for Underwater Acoustic using Conditional Convolutional Neural Netcited by 3
  5. 2024Scalable and Consistent Graph Neural Networks for Distributed Mesh-based Data-driven Modelingcited by 2
  6. 2024Harnessing Loss Decomposition for Long-Horizon Wave Predictions via Deep Neural Networkscited by 2
  7. 2025FIGNN: Feature-Specific Interpretability for Graph Neural Network Surrogate Modelscited by 2
  8. 2025Heterogeneous Graph Representation of Stiffened Panels with Non-Uniform Boundary Conditions and Loadscited by 2
  9. 2025Predicting Wave Dynamics using Deep Learning with Multistep Integration Inspired Attention and Physics-Based Loss Decompositioncited by 1
  10. 2026FEM-Informed Hypergraph Neural Networks for Efficient Elastoplasticitycited by 1
  11. 2025A Mesh-Adaptive Hypergraph Neural Network for Unsteady Flow Around Oscillating and Rotating Structurescited by 0
  12. 2026Multi-fidelity graph-based neural networks architectures to learn Navier-Stokes solutions on non-parametrized 2D domainscited by 0
2 more
  1. 2026An ALE-Consistent Graph Neural Operator-Transformer Framework for Fluid-Structure Interactioncited by 0
  2. 2026HGTO: A Unified Graph-Based Physics-Informed Formulation for Structural Topology Optimizationcited by 0