Learning Optimal Multigrid Smoothers via Neural Networks Article Swipe
Ru Huang
,
Ruipeng Li
,
Yuanzhe Xi
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.1137/21m1430030
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.1137/21m1430030
Multigrid methods are one of the most efficient techniques for solving large sparse linear systems arising from partial differential equations (PDEs) and graph Laplacians from machine learning applications. One of the key components of multigrid is smoothing, which aims at reducing high-frequency errors on each grid level. However, finding optimal smoothing algorithms is problem-dependent and can impose challenges for many problems. In this paper, we propose an efficient adaptive framework for learning optimized smoothers from operator stencils in the form of convolutional neural networks (CNNs). Here, the CNNs are trained on small-scale problems from a given type of PDEs based on a supervised loss function derived from multigrid convergence theories and can be applied to large-scale problems of the same class of PDEs. Numerical results on anisotropic rotated Laplacian problems and variable coefficient diffusion problems demonstrate improved convergence rates and solution time compared with classical hand-crafted relaxation methods.
Related Topics
Concepts
Multigrid method
Smoothing
Partial differential equation
Mathematics
Mathematical optimization
Artificial neural network
Relaxation (psychology)
Convergence (economics)
Applied mathematics
Computer science
Algorithm
Artificial intelligence
Mathematical analysis
Economic growth
Statistics
Economics
Psychology
Social psychology
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1137/21m1430030
- OA Status
- green
- Cited By
- 25
- References
- 32
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4297200229
All OpenAlex metadata
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https://openalex.org/W4297200229Canonical identifier for this work in OpenAlex
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https://doi.org/10.1137/21m1430030Digital Object Identifier
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Learning Optimal Multigrid Smoothers via Neural NetworksWork title
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2022Year of publication
- Publication date
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2022-08-24Full publication date if available
- Authors
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Ru Huang, Ruipeng Li, Yuanzhe XiList of authors in order
- Landing page
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https://doi.org/10.1137/21m1430030Publisher landing page
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
- OA URL
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https://www.osti.gov/biblio/2205730Direct OA link when available
- Concepts
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Multigrid method, Smoothing, Partial differential equation, Mathematics, Mathematical optimization, Artificial neural network, Relaxation (psychology), Convergence (economics), Applied mathematics, Computer science, Algorithm, Artificial intelligence, Mathematical analysis, Economic growth, Statistics, Economics, Psychology, Social psychologyTop concepts (fields/topics) attached by OpenAlex
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25Total citation count in OpenAlex
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2025: 12, 2024: 4, 2023: 6, 2022: 2, 2021: 1Per-year citation counts (last 5 years)
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10Other works algorithmically related by OpenAlex
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| referenced_works | https://openalex.org/W2005073368, https://openalex.org/W2165630134, https://openalex.org/W2770250658, https://openalex.org/W2070913801, https://openalex.org/W2075536798, https://openalex.org/W2106088594, https://openalex.org/W2962745910, https://openalex.org/W1987573671, https://openalex.org/W2012349161, https://openalex.org/W2001371530, https://openalex.org/W2078687549, https://openalex.org/W2038516134, https://openalex.org/W2025614228, https://openalex.org/W2803629276, https://openalex.org/W2912389156, https://openalex.org/W2158985775, https://openalex.org/W3008063637, https://openalex.org/W2884714875, https://openalex.org/W2791363721, https://openalex.org/W2130641059, https://openalex.org/W1901129140, https://openalex.org/W1506342804, https://openalex.org/W2749028154, https://openalex.org/W2963289862, https://openalex.org/W4211094263, https://openalex.org/W2945672665, https://openalex.org/W2033340616, https://openalex.org/W2963889991, https://openalex.org/W2963626582, https://openalex.org/W3102569296, https://openalex.org/W3100626142, https://openalex.org/W2014552949 |
| referenced_works_count | 32 |
| abstract_inverted_index.a | 94, 101 |
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| abstract_inverted_index.applications. | 27 |
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