mlsanityData to 7 Oct 2026

An Enhanced V-cycle MgNet Model for Operator Learning in Numerical Partial Differential Equations

arXiv 2302.00938 ↗First posted 2 Feb 2023cs.LG cs.NEcited by 4

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Abstract (arXiv)

This study used a multigrid-based convolutional neural network architecture known as MgNet in operator learning to solve numerical partial differential equations (PDEs). Given the property of smoothing iterations in multigrid methods where low-frequency errors decay slowly, we introduced a low-frequency correction structure for residuals to enhance the standard V-cycle MgNet. The enhanced MgNet model can capture the low-frequency features of solutions considerably better than the standard V-cycle MgNet. The numerical results obtained using some standard operator learning tasks are better than those obtained using many state-of-the-art methods, demonstrating the efficiency of our model.Moreover, numerically, our new model is more robust in case of low- and high-resolution data during training and testing, respectively.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 24 of its 49 references that are in the map. First posted on arXiv 2 Feb 2023.

Builds on

24 of 49 references.

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12 more
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Cited by year

Citing papers per year: 2023: 1; 2024: 1; 2025: 2.

4 papers.

  1. 2023MgNO: Efficient Parameterization of Linear Operators via Multigridcited by 40
  2. 2025Orthogonal greedy algorithm for linear operator learning with shallow neural networkcited by 3
  3. 2025Self-composing neural operators for high-frequency and multiscale PDE surrogatescited by 3
  4. 2024A MgNO Method for Multiphase Flow in Porous Mediacited by 2