MGIC: Multigrid-in-Channels Neural Network Architectures

DOI10.1137/21m1430194arXiv2011.09128OpenAlexW3205071126MaRDI QIDQ6108155

Lars Ruthotto, Moshe Eliasof, Unnamed Author, Eran Treister

Publication date: 29 June 2023

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.09128

zbMATH Keywords

alternative CNN architecturescompact and lightweight neural networksmultilevel neural networks

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Artificial neural networks and deep learning (68T07) Machine vision and scene understanding (68T45)

Cites Work

• Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• MgNet: a unified framework of multigrid and convolutional neural network
• A Multilevel Framework for Sparse Optimization with Application to Inverse Covariance Estimation and Logistic Regression
• Lean Algebraic Multigrid (LAMG): Fast Graph Laplacian Linear Solver
• Multilevel Adaptive Aggregation for Markov Chains, with Application to Web Ranking
• Multigrid Methods for PDE Optimization
• A Multigrid Tutorial, Second Edition
• Layer-Parallel Training of Deep Residual Neural Networks
• DeepXDE: A Deep Learning Library for Solving Differential Equations
• Parallel Time Integration with Multigrid
• fPINNs: Fractional Physics-Informed Neural Networks
• SwitchNet: A Neural Network Model for Forward and Inverse Scattering Problems
• An Efficient Multigrid Method for Graph Laplacian Systems II: Robust Aggregation
• Strong Solutions for PDE-Based Tomography by Unsupervised Learning
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