Error estimates and physics informed augmentation of neural networks for thermally coupled incompressible Navier Stokes equations

DOI10.1007/s00466-023-02334-7zbMath1523.76077arXiv2209.02977MaRDI QIDQ6109270

Arif Masud, Shoaib Goraya, Nahil Atef Sobh

Publication date: 27 July 2023

Published in: Computational Mechanics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2209.02977

zbMATH Keywords

convergencemachine learningBeltrami flowphysics informed augmentation

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Learning and adaptive systems in artificial intelligence (68T05) Navier-Stokes equations for incompressible viscous fluids (76D05) Basic methods in fluid mechanics (76M99)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A multiscale/stabilized finite element method for the advection-diffusion equation
• A variational multiscale stabilized formulation for the incompressible Navier-Stokes equations
• Multilayer feedforward networks are universal approximators
• Bayesian deep convolutional encoder-decoder networks for surrogate modeling and uncertainty quantification
• Variationally derived discontinuity capturing methods: fine scale models with embedded weak and strong discontinuities
• Machine learning in cardiovascular flows modeling: predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks
• Deep UQ: learning deep neural network surrogate models for high dimensional uncertainty quantification
• DGM: a deep learning algorithm for solving partial differential equations
• Machine learning materials physics: multi-resolution neural networks learn the free energy and nonlinear elastic response of evolving microstructures
• A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics
• Solution of physics-based Bayesian inverse problems with deep generative priors
• NSFnets (Navier-Stokes flow nets): physics-informed neural networks for the incompressible Navier-Stokes equations
• PhyGeoNet: physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain
• Physics-informed neural networks for high-speed flows
• Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks
• Residual-based closure model for density-stratified incompressible turbulent flows
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• A multiscale finite element method for the incompressible Navier-Stokes equations
• A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code
• Numerical simulation of two‐dimensional laminar mixed‐convection in a lid‐driven cavity using the mixed finite element consistent splitting scheme
• Neural‐network‐based approximations for solving partial differential equations
• Deep learning of vortex-induced vibrations
• Ill-Conditioning in Neural Network Training Problems
• Applied Analysis of the Navier-Stokes Equations
• Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs
• On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs
• The Method of Weighted Residuals and Variational Principles

This page was built for publication: Error estimates and physics informed augmentation of neural networks for thermally coupled incompressible Navier Stokes equations