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First-order PDES for Graph Neural Networks: Advection And Burgers Equation Models

arXiv 2404.03081 ↗First posted 3 Apr 2024cs.LG cs.NA math.NAcited by 0

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Abstract (arXiv)

Graph Neural Networks (GNNs) have established themselves as the preferred methodology in a multitude of domains, ranging from computer vision to computational biology, especially in contexts where data inherently conform to graph structures. While many existing methods have endeavored to model GNNs using various techniques, a prevalent challenge they grapple with is the issue of over-smoothing. This paper presents new Graph Neural Network models that incorporate two first-order Partial Differential Equations (PDEs). These models do not increase complexity but effectively mitigate the over-smoothing problem. Our experimental findings highlight the capacity of our new PDE model to achieve comparable results with higher-order PDE models and fix the over-smoothing problem up to 64 layers. These results underscore the adaptability and versatility of GNNs, indicating that unconventional approaches can yield outcomes on par with established techniques.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 19 of its 26 references that are in the map. First posted on arXiv 3 Apr 2024.

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19 of 26 references.

References · 19

  1. 2017Inductive Representation Learning on Large Graphscited by 6,284
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  3. 2019Simplifying Graph Convolutional Networkscited by 1,470
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  7. 2020Simple and Deep Graph Convolutional Networkscited by 857
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  9. 2020Geom-GCN: Geometric Graph Convolutional Networkscited by 821
  10. 2015Convolutional Networks on Graphs for Learning Molecular Fingerprintscited by 751
  11. 2019Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological Viewcited by 544
  12. 2016Geometric deep learning on graphs and manifolds using mixture model CNNscited by 468
7 more
  1. 2019PairNorm: Tackling Oversmoothing in GNNscited by 297
  2. 2021GRAND: Graph Neural Diffusioncited by 258
  3. 2020Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Predictioncited by 137
  4. 2021PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equationscited by 106
  5. 2019Improving Graph Attention Networks with Large Margin-based Constraintscited by 34
  6. 2022Improving Graph Neural Networks with Learnable Propagation Operatorscited by 19
  7. 2020DiffGCN: Graph Convolutional Networks via Differential Operators and Algebraic Multigrid Poolingcited by 16

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