ConvStabNet: a CNN-based approach for the prediction of local stabilization parameter for SUPG scheme

Abstract

This paper presents ConvStabNet, a convolutional neural network designed to predict optimal stabilization parameters for each cell in the Streamline Upwind Petrov Galerkin (SUPG) stabilization scheme. ConvStabNet employs a shared parameter approach, allowing the network to understand the relationships between cell characteristics and their corresponding stabilization parameters while efficiently handling the parameter space. Comparative analyses with state-of-the-art neural network solvers based on variational formulations highlight the superior performance of ConvStabNet. To improve the accuracy of SUPG in solving partial differential equations (PDEs) with interior and boundary layers, ConvStabNet incorporates a loss function that combines a strong residual component with a cross-wind derivative term. The findings confirm ConvStabNet as a promising method for accurately predicting stabilization parameters in SUPG, thereby marking it as an advancement over neural network-based PDE solvers.