An enhanced V-cycle MgNet model for operator learning in numerical partial differential equations

Jianqing Zhu, Juncai He, Qiumei Huang

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish (US)
JournalComputational Geosciences
StatePublished - Jul 1 2023

Bibliographical note

KAUST Repository Item: Exported on 2023-07-04
Acknowledgements: We would like to thank Jinchao Xu for these valuable discussions and comments. The work of the first and third authors was supported in part by Beijing Natural Science Foundation Project No. Z200002. The work of the second author was supported by the KAUST Baseline Research Fund.

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computational Mathematics
  • Computers in Earth Sciences
  • Computer Science Applications


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