Meta-mgnet: meta multigrid networks for solving parameterized partial differential equations

DOI10.1016/j.jcp.2022.110996OpenAlexW4226429807WikidataQ114163364 ScholiaQ114163364MaRDI QIDQ2133752

Yuyan Chen, Bin Dong, Jin-Chao Xu

Publication date: 5 May 2022

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.14088

zbMATH Keywords

multigridmeta-learningdeep-learningmgnetparameterized PDEs

Mathematics Subject Classification ID

Basic methods in fluid mechanics (76Mxx) Artificial intelligence (68Txx) Numerical methods for partial differential equations, boundary value problems (65Nxx)

Related Items

Learning-based local weighted least squares for algebraic multigrid method, AI‐enhanced iterative solvers for accelerating the solution of large‐scale parametrized systems, Side effects of learning from low-dimensional data embedded in a Euclidean space

Uses Software

• torchdiffeq
• MgNet
• DGM
• MetaInv-Net
• MscaleDNN

Cites Work

• Unnamed Item
• MetaInv-Net
• The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
• DGM: a deep learning algorithm for solving partial differential equations
• DLGA-PDE: discovery of PDEs with incomplete candidate library via combination of deep learning and genetic algorithm
• Detecting troubled-cells on two-dimensional unstructured grids using a neural network
• A mesh-free method for interface problems using the deep learning approach
• Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders
• MgNet: a unified framework of multigrid and convolutional neural network
• Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations
• Convergence analysis of triangular MAC schemes for two dimensional Stokes equations
• A proposal on machine learning via dynamical systems
• A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
• Analysis of a two-level method for anisotropic diffusion equations on aligned and nonaligned grids
• Reduced-order modeling of parameterized PDEs using time-space-parameter principal component analysis
• Sharp Estimates for Multigrid Rates of Convergence with General Smoothing and Acceleration
• Iterative Methods by Space Decomposition and Subspace Correction
• The method of alternating projections and the method of subspace corrections in Hilbert space
• Algebraic multigrid methods
• Stable architectures for deep neural networks
• Analysis and convergence of the MAC scheme. II. Navier-Stokes equations
• Solving high-dimensional partial differential equations using deep learning
• Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains
• Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks