Predicting the Stabilization Quantity with Neural Networks for Singularly Perturbed Partial Differential Equations
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). The proposed method has been observed to yield accurate results and even outperform 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. "Predicting the Stabilization Quantity with Neural Networks for Singularly Perturbed Partial Differential Equations." ICML 2023 Workshops: SynS_and_ML, 2023.Markdown
[Yadav. "Predicting the Stabilization Quantity with Neural Networks for Singularly Perturbed Partial Differential Equations." ICML 2023 Workshops: SynS_and_ML, 2023.](https://mlanthology.org/icmlw/2023/yadav2023icmlw-predicting/)BibTeX
@inproceedings{yadav2023icmlw-predicting,
title = {{Predicting the Stabilization Quantity with Neural Networks for Singularly Perturbed Partial Differential Equations}},
author = {Yadav, Sangeeta},
booktitle = {ICML 2023 Workshops: SynS_and_ML},
year = {2023},
url = {https://mlanthology.org/icmlw/2023/yadav2023icmlw-predicting/}
}