DNN-MG: a hybrid neural network/finite element method with applications to 3D simulations of the Navier-Stokes equations
From MaRDI portal
Publication:6194150
DOI10.1016/j.cma.2023.116692arXiv2307.14837OpenAlexW4390085660MaRDI QIDQ6194150
No author found.
Publication date: 19 March 2024
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2307.14837
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
- A finite element pressure gradient stabilization for the Stokes equations based on local projections
- Fluid-structure interactions. Models, analysis and finite elements
- A priori and a posteriori error estimates for the deep Ritz method applied to the Laplace and Stokes problem
- A theoretical analysis of deep neural networks and parametric PDEs
- Hybrid FEM-NN models: combining artificial neural networks with the finite element method
- A neural network multigrid solver for the Navier-Stokes equations
- Scientific machine learning through physics-informed neural networks: where we are and what's next
- An assessment of some solvers for saddle point problems emerging from the incompressible Navier-Stokes equations
- MgNet: a unified framework of multigrid and convolutional neural network
- Stabilized finite element methods for the generalized Oseen problem
- Solutions of 3D Navier-Stokes benchmark problems with adaptive finite elements
- Accelerating high order discontinuous Galerkin solvers using neural networks: 1D Burgers' equation
- Surrogate convolutional neural network models for steady computational fluid dynamics simulations
- Finite element approximation of wave problems with correcting terms based on training artificial neural networks with fine solutions
- Neural control of discrete weak formulations: Galerkin, least squares \& minimal-residual methods with quasi-optimal weights
- Parallel multigrid method for finite element simulations of complex flow problems on locally refined meshes
- The post-processing approach in the finite element method—Part 2: The calculation of stress intensity factors
- Finite-Element Approximation of the Nonstationary Navier–Stokes Problem. Part IV: Error Analysis for Second-Order Time Discretization
- Multigrid techniques for finite elements on locally refined meshes
- Galerkin Neural Networks: A Framework for Approximating Variational Equations with Error Control
- DeepXDE: A Deep Learning Library for Solving Differential Equations
- Stationary Flow Predictions Using Convolutional Neural Networks
- ARTIFICIAL BOUNDARIES AND FLUX AND PRESSURE CONDITIONS FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS
- Learning physics-based models from data: perspectives from inverse problems and model reduction
- Transformers for modeling physical systems
- The \texttt{deal.II} library, version 9.5
- Accelerating high order discontinuous Galerkin solvers using neural networks: 3D compressible Navier-Stokes equations
- Learning Optimal Multigrid Smoothers via Neural Networks
- Semi-supervised invertible neural operators for Bayesian inverse problems
