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

Abstract

We propose 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 modelled 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).

Tasks

Reproductions