A neural network multigrid solver for the Navier-Stokes equations
From MaRDI portal
Publication:2137963
DOI10.1016/j.jcp.2022.110983OpenAlexW3080730553MaRDI QIDQ2137963
Publication date: 11 May 2022
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2008.11520
Basic methods in fluid mechanics (76Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Incompressible viscous fluids (76Dxx)
Related Items (9)
A Model-Constrained Tangent Slope Learning Approach for Dynamical Systems ⋮ Solving the discretised neutron diffusion equations using neural networks ⋮ Hierarchical subspace evolution method for super large parallel computing: A linear solver and an eigensolver as examples ⋮ Development of three-dimensional rotated lattice Boltzmann flux solver for the simulation of high-speed compressible flows ⋮ A conservative hybrid deep learning method for Maxwell-Ampère-Nernst-Planck equations ⋮ Connections between numerical algorithms for PDEs and neural networks ⋮ DNN-MG: a hybrid neural network/finite element method with applications to 3D simulations of the Navier-Stokes equations ⋮ Approximation of optimal control problems for the Navier-Stokes equation via multilinear HJB-POD ⋮ A priori and a posteriori error estimates for the deep Ritz method applied to the Laplace and Stokes problem
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- An efficient fluid-solid coupling algorithm for single-phase flows
- Block-implicit multigrid solution of Navier-Stokes equations in primitive variables
- Approximation and estimation bounds for artificial neural networks
- Hidden physics models: machine learning of nonlinear partial differential equations
- 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
- Sympnets: intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems
- A Newton multigrid framework for optimal control of fluid-structure interactions
- A theoretical analysis of deep neural networks and parametric PDEs
- Data-driven discovery of PDEs in complex datasets
- Data driven governing equations approximation using deep neural networks
- Modeling the dynamics of PDE systems with physics-constrained deep auto-regressive networks
- Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks
- Stabilized finite element methods for the generalized Oseen problem
- Finite-Element Approximation of the Nonstationary Navier–Stokes Problem. Part IV: Error Analysis for Second-Order Time Discretization
- Machine learning the kinematics of spherical particles in fluid flows
- Deep Splitting Method for Parabolic PDEs
- Parallel Multigrid on Locally Refined Meshes
- Parallel time-stepping for fluid–structure interactions
- Optimal Approximation with Sparsely Connected Deep Neural Networks
- Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks
- Data-Driven Identification of Parametric Partial Differential Equations
- ARTIFICIAL BOUNDARIES AND FLUX AND PRESSURE CONDITIONS FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS
- Approximation by superpositions of a sigmoidal function
This page was built for publication: A neural network multigrid solver for the Navier-Stokes equations
