mlsanityData to 7 Oct 2026

Understanding the Efficacy of U-Net & Vision Transformer for Groundwater Numerical Modelling

arXiv 2307.04010 ↗First posted 8 Jul 2023physics.flu-dyn cs.CE cs.LGcited by 2

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Abstract (arXiv)

This paper presents a comprehensive comparison of various machine learning models, namely U-Net, U-Net integrated with Vision Transformers (ViT), and Fourier Neural Operator (FNO), for time-dependent forward modelling in groundwater systems. Through testing on synthetic datasets, it is demonstrated that U-Net and U-Net + ViT models outperform FNO in accuracy and efficiency, especially in sparse data scenarios. These findings underscore the potential of U-Net-based models for groundwater modelling in real-world applications where data scarcity is prevalent.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 14 of its 21 references that are in the map. First posted on arXiv 8 Jul 2023.

Builds on

14 of 21 references.

References · 14

  1. 2017Attention Is All You Needcited by 59,932
  2. 2020An Image is Worth 16x16 Words: Transformers for Image Recognition at Scalecited by 29,915
  3. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  4. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  5. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  6. 2021TransUNet: Transformers Make Strong Encoders for Medical Image Segmentationcited by 1,552
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  8. 2021Choose a Transformer: Fourier or Galerkincited by 333
  9. 2021U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flowcited by 292
  10. 2022Transformer for Partial Differential Equations' Operator Learningcited by 270
  11. 2022Towards Multi-spatiotemporal-scale Generalized PDE Modelingcited by 190
  12. 2022NOMAD: Nonlinear Manifold Decoders for Operator Learningcited by 81
2 more
  1. 2023Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestrationcited by 46
  2. 2023ViTO: Vision Transformer-Operatorcited by 29

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Citing papers per year: 2024: 1; 2025: 0; 2026: 1.

2 papers.