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

Sangeeta Yadav (Indian Institute of Science)*; Sashikumaar Ganesan (Indian Institute of Science)


Numerical techniques and neural network-based PDE solvers are both inadequate to solve singularly perturbed differential equations(SPDE). Both of these techniques give spurious oscillation in the numerical solution in the presence of boundary layers. Stabilization techniques are often employed to reduce spurious oscillations, but the accuracy of the stabilization technique is limited by the availability of a user-chosen stabilization parameter. Here we propose SPDE-Net, a novel artificial neural network(ANN) to predict the stabilization parameter for Streamline-Upwind Petrov-Galerkin(SUPG) stabilization technique for solving SPDEs. The prediction task is modeled as a regression problem and is solved using ANNs. Three variants of training have been proposed i.e supervised, L^2 Error Minimization(global) and L^2 Error Minimization(local). All of the proposed techniques, perform better than state-of-the-art neural network based PDE solvers.