SPDE-Net: Neural Network Based Prediction of Stabilization Parameter for SUPG Technique
Abstract
We propose \textit{SPDE-Net}, an artificial neural network (ANN) to predict the stabilization parameter for the streamline upwind/Petrov-Galerkin (SUPG) stabilization technique for solving singularly perturbed differential equations (SPDEs). The prediction task is modeled as a regression problem and is solved using ANN. Three training strategies for the ANN have been proposed i.e supervised, $L^2$ error minimization (global) and $L^2$ error minimization (local). It has been observed that the proposed method yields accurate results, and even outperforms some of the existing state-of-the-art ANN-based partial differential equation (PDE) solvers such as Physics Informed Neural Network (PINN).
Cite
Text
Yadav and Ganesan. "SPDE-Net: Neural Network Based Prediction of Stabilization Parameter for SUPG Technique." Proceedings of The 13th Asian Conference on Machine Learning, 2021.Markdown
[Yadav and Ganesan. "SPDE-Net: Neural Network Based Prediction of Stabilization Parameter for SUPG Technique." Proceedings of The 13th Asian Conference on Machine Learning, 2021.](https://mlanthology.org/acml/2021/yadav2021acml-spdenet/)BibTeX
@inproceedings{yadav2021acml-spdenet,
title = {{SPDE-Net: Neural Network Based Prediction of Stabilization Parameter for SUPG Technique}},
author = {Yadav, Sangeeta and Ganesan, Sashikumaar},
booktitle = {Proceedings of The 13th Asian Conference on Machine Learning},
year = {2021},
pages = {268-283},
volume = {157},
url = {https://mlanthology.org/acml/2021/yadav2021acml-spdenet/}
}