PhyGeoNet
swMATH ID:  44440 
Software Authors:  Gao, Han; Sun, Luning; Wang, JianXun 
Description:  PhyGeoNet: physicsinformed geometryadaptive convolutional neural networks for solving parameterized steadystate PDEs on irregular domain. Recently, the advent of deep learning has spurred interest in the development of physicsinformed neural networks (PINN) for efficiently solving partial differential equations (PDEs), particularly in a parametric setting. Among all different classes of deep neural networks, the convolutional neural network (CNN) has attracted increasing attention in the scientific machine learning community, since the parametersharing feature in CNN enables efficient learning for problems with largescale spatiotemporal fields. However, one of the biggest challenges is that CNN only can handle regular geometries with imagelike format (i.e., rectangular domains with uniform grids). In this paper, we propose a novel physicsconstrained CNN learning architecture, aiming to learn solutions of parametric PDEs on irregular domains without any labeled data. In order to leverage powerful classic CNN backbones, elliptic coordinate mapping is introduced to enable coordinate transforms between the irregular physical domain and regular reference domain. The proposed method has been assessed by solving a number of steadystate PDEs on irregular domains, including heat equations, NavierStokes equations, and Poisson equations with parameterized boundary conditions, varying geometries, and spatiallyvarying source fields. Moreover, the proposed method has also been compared against the stateoftheart PINN with fullyconnected neural network (FCNN) formulation. The numerical results demonstrate the effectiveness of the proposed approach and exhibit notable superiority over the FCNN based PINN in terms of efficiency and accuracy. 
Homepage:  https://github.com/JianxunWang/phygeonet 
Source Code:  https://github.com/JianxunWang/phygeonet 
Dependencies:  C++ 
Keywords:  physicsinformed neural networks; labelfree; surrogate modeling; physicsconstrained deep learning; partial differential equations; NavierStokes 
Related Software:  Adam; NSFnets; hpVPINNs; DiffSharp; DGM; DeepXDE; DeepONet; PyTorch; TensorFlow; XPINNs; PINNsNTK; FPINNs; PPINN; PhyCRNet; PDENet; LBFGS; D3M; UNet; PhyCNN; VarNet 
Cited in:  52 Documents 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

PhyGeoNet: physicsinformed geometryadaptive convolutional neural networks for solving parameterized steadystate PDEs on irregular domain. Zbl 07511433 Gao, Han; Sun, Luning; Wang, JianXun 
2021

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Cited by 158 Authors
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Cited in 17 Serials
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