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Author:

Zhu, Jianqing (Zhu, Jianqing.) | He, Juncai (He, Juncai.) | Huang, Qiumei (Huang, Qiumei.) (Scholars:黄秋梅)

Indexed by:

Scopus SCIE

Abstract:

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.

Keyword:

Low-frequency correction Numerical partial differential equations Operator learning MgNet

Author Community:

  • [ 1 ] [Zhu, Jianqing]Beijing Univ Technol, Fac Sci, Beijing 100124, Chaoyang, Peoples R China
  • [ 2 ] [Huang, Qiumei]Beijing Univ Technol, Fac Sci, Beijing 100124, Chaoyang, Peoples R China
  • [ 3 ] [He, Juncai]King Abdullah Univ Sci & Technol KAUST, Comp Elect & Math Sci & Engn Div, Thuwal 239556900, Saudi Arabia

Reprint Author's Address:

  • [Huang, Qiumei]Beijing Univ Technol, Fac Sci, Beijing 100124, Chaoyang, Peoples R China;;

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Source :

COMPUTATIONAL GEOSCIENCES

ISSN: 1420-0597

Year: 2023

Issue: 5

Volume: 28

Page: 809-820

ESI Discipline: COMPUTER SCIENCE;

ESI HC Threshold:19

Cited Count:

WoS CC Cited Count: 0

SCOPUS Cited Count:

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 0

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