DNN-MG: a hybrid neural network/finite element method with applications to 3D simulations of the Navier-Stokes equations (Q6194150)

scientific article; zbMATH DE number 7820238

Language	Label	Description	Also known as
English	DNN-MG: a hybrid neural network/finite element method with applications to 3D simulations of the Navier-Stokes equations	scientific article; zbMATH DE number 7820238

Statements

instance of

scholarly article

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title

DNN-MG: a hybrid neural network/finite element method with applications to 3D simulations of the Navier-Stokes equations (English)

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published in

Computer Methods in Applied Mechanics and Engineering

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publication date

19 March 2024

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full work available at URL

https://arxiv.org/abs/2307.14837

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zbMATH Keywords

geometric multigrid methods

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deep neural network

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Navier-Stokes equations

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machine learning

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MaRDI profile type

MaRDI publication profile

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cites work

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Semi-supervised invertible neural operators for Bayesian inverse problems

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A neural network multigrid solver for the Navier-Stokes equations

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Stationary Flow Predictions Using Convolutional Neural Networks

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Surrogate convolutional neural network models for steady computational fluid dynamics simulations

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Learning physics-based models from data: perspectives from inverse problems and model reduction

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A priori and a posteriori error estimates for the deep Ritz method applied to the Laplace and Stokes problem

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Accelerating high order discontinuous Galerkin solvers using neural networks: 1D Burgers' equation

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Accelerating high order discontinuous Galerkin solvers using neural networks: 3D compressible Navier-Stokes equations

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Finite element approximation of wave problems with correcting terms based on training artificial neural networks with fine solutions

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Neural control of discrete weak formulations: Galerkin, least squares \& minimal-residual methods with quasi-optimal weights

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Galerkin Neural Networks: A Framework for Approximating Variational Equations with Error Control

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Hybrid FEM-NN models: combining artificial neural networks with the finite element method

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MgNet: a unified framework of multigrid and convolutional neural network

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Learning Optimal Multigrid Smoothers via Neural Networks

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Fluid-structure interactions. Models, analysis and finite elements

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A finite element pressure gradient stabilization for the Stokes equations based on local projections

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Q4823208

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Stabilized finite element methods for the generalized Oseen problem

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Finite-Element Approximation of the Nonstationary Navier–Stokes Problem. Part IV: Error Analysis for Second-Order Time Discretization

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Q4841246

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Multigrid techniques for finite elements on locally refined meshes

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Q4338821

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Solutions of 3D Navier-Stokes benchmark problems with adaptive finite elements

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The \texttt{deal.II} library, version 9.5

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ARTIFICIAL BOUNDARIES AND FLUX AND PRESSURE CONDITIONS FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

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The post-processing approach in the finite element method—Part 2: The calculation of stress intensity factors

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Parallel multigrid method for finite element simulations of complex flow problems on locally refined meshes

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An assessment of some solvers for saddle point problems emerging from the incompressible Navier-Stokes equations

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Identifiers

arXiv ID

2307.14837

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DOI

10.1016/j.cma.2023.116692

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:6194150