Mosaic flows: a transferable deep learning framework for solving PDEs on unseen domains
type: Item
instance of: scholarly article
title: Mosaic flows: a transferable deep learning framework for solving PDEs on unseen domains
author: Hengjie Wang
author: Robert Planas
author: Aparna Chandramowlishwaran
author: Ramin Bostanabad
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 2022-01-26T00:00:00Z
full work available at URL: https://arxiv.org/abs/2104.10873
Mathematics Subject Classification ID: 65M99
Mathematics Subject Classification ID: 68T07
zbMATH DE Number: 7464526
zbMATH Keywords: neural networks
zbMATH Keywords: transferable deep learning
zbMATH Keywords: scientific machine learning
zbMATH Keywords: PDEs
zbMATH Keywords: Navier-Stokes equations
describes a project that uses: FPINNs
describes a project that uses: PINNsNTK
describes a project that uses: NSFnets
describes a project that uses: PyAMG
describes a project that uses: PyTorch
describes a project that uses: Adam
describes a project that uses: GPyTorch
describes a project that uses: TensorFlow
describes a project that uses: L-BFGS
describes a project that uses: PPINN
describes a project that uses: DeepONet
describes a project that uses: XPINNs
describes a project that uses: hp-VPINNs
describes a project that uses: F3DAM
describes a project that uses: OpenFOAM
describes a project that uses: rpart
describes a project that uses: Xception
describes a project that uses: U-Net
describes a project that uses: GitHub
MaRDI profile type: Publication
OpenAlex ID: W3205765690
Wikidata QID: Q114196861
cites work: Nonlinear finite elements for continua and structures
cites work: Predicting the output from a complex computer code when fast approximations are available
cites work: Q3394879
cites work: Q5169898
cites work: Q5270493
cites work: Hierarchical deep learning neural network (HiDeNN): an artificial intelligence (AI) framework for computational science and engineering
cites work: Deep generative modeling for mechanistic-based learning and design of metamaterial systems
cites work: Data-driven learning of nonlocal physics from high-fidelity synthetic data
cites work: Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
cites work: Q3474197
cites work: Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations
cites work: Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations
cites work: \textit{hp}-VPINNs: variational physics-informed neural networks with domain decomposition
cites work: PPINN: parareal physics-informed neural network for time-dependent PDEs
cites work: Data-driven deep learning of partial differential equations in modal space
cites work: Prediction of aerodynamic flow fields using convolutional neural networks
cites work: Modeling the dynamics of PDE systems with physics-constrained deep auto-regressive networks
cites work: Bayesian deep convolutional encoder-decoder networks for surrogate modeling and uncertainty quantification
cites work: Quantifying model form uncertainty in Reynolds-averaged turbulence models with Bayesian deep neural networks
cites work: Reynolds averaged turbulence modelling using deep neural networks with embedded invariance
cites work: The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
cites work: fPINNs: Fractional Physics-Informed Neural Networks
cites work: Iterative Methods by Space Decomposition and Subspace Correction
cites work: Domain decomposition methods for the numerical solution of partial differential equations
cites work: NSFnets (Navier-Stokes flow nets): physics-informed neural networks for the incompressible Navier-Stokes equations
cites work: On the limited memory BFGS method for large scale optimization
cites work: An overlapping Schwarz method for spectral element solution of the incompressible Navier-Stokes equations
cites work: Q4944031
cites work: Hybrid Schwarz-Multigrid Methods for the Spectral Element Method: Extensions to Navier-Stokes
cites work: Towards optimized Schwarz methods for the Navier-Stokes equations
cites work: Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
cites work: Large-Scale Machine Learning with Stochastic Gradient Descent
cites work: Quantifying the generalization error in deep learning in terms of data distribution and neural network smoothness
cites work: Q4277561
cites work: Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data
DOI: 10.1016/J.CMA.2021.114424
description: scientific article; zbMATH DE number 7464526