Multi-Scale Deep Neural Network (MscaleDNN) Methods for Oscillatory Stokes Flows in Complex Domains

DOI10.4208/cicp.OA-2020-0192zbMath1473.35541arXiv2009.12729MaRDI QIDQ5162374

Bo Wang, Wenzhong Zhang, Wei Cai

Publication date: 2 November 2021

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

Full work available at URL: https://arxiv.org/abs/2009.12729

zbMATH Keywords

meshless methodsStokes equationmulti-scaledeep neural network

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Basic methods in fluid mechanics (76M99) Numerical methods for partial differential equations, boundary value problems (65N99) PDEs in connection with computer science (35Q68)

Related Items (9)

Generalization Error Analysis of Neural Networks with Gradient Based Regularization ⋮ VPVnet: A Velocity-Pressure-Vorticity Neural Network Method for the Stokes’ Equations under Reduced Regularity ⋮ Three ways to solve partial differential equations with neural networks — A review ⋮ Linearized Learning with Multiscale Deep Neural Networks for Stationary Navier-Stokes Equations with Oscillatory Solutions ⋮ Isogeometric neural networks: a new deep learning approach for solving parameterized partial differential equations ⋮ Subspace decomposition based DNN algorithm for elliptic type multi-scale PDEs ⋮ Deep Nitsche Method: Deep Ritz Method with Essential Boundary Conditions ⋮ A Local Deep Learning Method for Solving High Order Partial Differential Equations ⋮ A deep domain decomposition method based on Fourier features

Uses Software

• Adam
• MscaleDNN
• NSFnets

Cites Work

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• Boundary conditions for incompressible flows
• Spectral element simulations of laminar and turbulent flows in complex geometries
• High-order splitting methods for the incompressible Navier-Stokes equations
• The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires. II
• Gauge method for viscous incompressible flows
• Finite Element Methods for Navier-Stokes Equations
• Ten Lectures on Wavelets
• Finite Element Methods of Least-Squares Type
• Solving high-dimensional partial differential equations using deep learning
• A Phase Shift Deep Neural Network for High Frequency Approximation and Wave Problems
• On the Convergence of Discrete Approximations to the Navier-Stokes Equations

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