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, L2 error minimization (global) and L2 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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