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Artificial neural network-augmented stabilized finite element method
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DOI：10.1016/j.jcp.2023.112702.png)
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摘要
En 中文
An artificial neural network-augmented Streamline Upwind/Petrov-Galerkin finite element scheme (SPDE-NetII) is proposed for solving singularly perturbed partial differential equations. In particular, an artificial neural network framework is proposed to predict optimal values for the stabilization parameter to be used in Streamline upwind/Petrov-Galerkin stabilization schemes. The neural network is trained by minimizing a physics-informed cost function, where the equation's mesh and physical parameters are used as input features. Further, the predicted stabilization parameter is normalized with the gradient of the solution to treat the boundary/interior layer region adequately. The proposed approach suppresses the undershoots and overshoots in the stabilized finite element solution and outperforms the existing neural network-based partial differential equation solvers such as Physics-Informed Neural Networks and Variational Neural Networks.
Keyword:
Singularly perturbed partial differential equations
Streamline upwind/Petrov-Galerkin
Finite element method
Artificial neural network
Physics Informed Neural Network
Stabilization schemes
期刊
IF:
3.8
论文数:
1.6W
被引数:
7.4W
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