Predicting the stabilization quantity with neural networks for Singularly Perturbed Partial Differential Equations

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).