The deep learning Galerkin method for the general Stokes equations

DOI10.1007/s10915-022-01930-8OpenAlexW3088619209MaRDI QIDQ2674271

Wen Zhang, Jing Yue, Jian Li, Wan-Suo Duan

Publication date: 22 September 2022

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.11701

zbMATH Keywords

convergenceneural networkdeep learningdeep Galerkin methodgeneral Stokes equations

Mathematics Subject Classification ID

Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Fluid mechanics (76-XX)

Related Items (6)

Numerical Solution of the Incompressible Navier-Stokes Equation by a Deep Branching Algorithm ⋮ Deep neural network solution for finite state mean field game with error estimation ⋮ The robust physics-informed neural networks for a typical fourth-order phase field model ⋮ CPINNs: a coupled physics-informed neural networks for the closed-loop geothermal system ⋮ Unnamed Item ⋮ Efficient coupled deep neural networks for the time-dependent coupled Stokes-Darcy problems

Uses Software

• TensorFlow
• DeepXDE
• DGM
• FPINNs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlinear parabolic equations with measure data
• Inferring solutions of differential equations using noisy multi-fidelity data
• Machine learning of linear differential equations using Gaussian processes
• Bayesian deep convolutional encoder-decoder networks for surrogate modeling and uncertainty quantification
• Numerical solution of damped nonlinear Klein--Gordon equations using variational method and finite element approach
• DGM: a deep learning algorithm for solving partial differential equations
• Finite volume methods for the incompressible Navier-Stokes equations
• B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data
• DLGA-PDE: discovery of PDEs with incomplete candidate library via combination of deep learning and genetic algorithm
• Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data
• Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations
• Superconvergence of discontinuous Galerkin finite element method for the stationary Navier-Stokes equations
• Stochastic Gradient Descent in Continuous Time
• Topology optimization of fluids in Stokes flow
• DeepXDE: A Deep Learning Library for Solving Differential Equations
• Model Reduction with Memory and the Machine Learning of Dynamical Systems
• On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs
• Physics-Informed Neural Networks with Hard Constraints for Inverse Design
• fPINNs: Fractional Physics-Informed Neural Networks
• Neural network method for solving partial differential equations

This page was built for publication: The deep learning Galerkin method for the general Stokes equations