SPDE-Net: Neural Network based prediction of stabilization parameter for SUPG technique

Sangeeta Yadav, Sashikumaar Ganesan
Proceedings of The 13th Asian Conference on Machine Learning, PMLR 157:268-283, 2021.

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 this Paper

BibTeX
@InProceedings{pmlr-v157-yadav21a, 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}, pages = {268--283}, year = {2021}, editor = {Balasubramanian, Vineeth N. and Tsang, Ivor}, volume = {157}, series = {Proceedings of Machine Learning Research}, month = {17--19 Nov}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v157/yadav21a/yadav21a.pdf}, url = {https://proceedings.mlr.press/v157/yadav21a.html}, 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).} }
Endnote
%0 Conference Paper %T SPDE-Net: Neural Network based prediction of stabilization parameter for SUPG technique %A Sangeeta Yadav %A Sashikumaar Ganesan %B Proceedings of The 13th Asian Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Vineeth N. Balasubramanian %E Ivor Tsang %F pmlr-v157-yadav21a %I PMLR %P 268--283 %U https://proceedings.mlr.press/v157/yadav21a.html %V 157 %X 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).
APA
Yadav, S. & Ganesan, S.. (2021). SPDE-Net: Neural Network based prediction of stabilization parameter for SUPG technique. Proceedings of The 13th Asian Conference on Machine Learning, in Proceedings of Machine Learning Research 157:268-283 Available from https://proceedings.mlr.press/v157/yadav21a.html.

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