OPTIMIZING STABILIZATION IN SINGULARLY PER- TURBED PROBLEMS WITH SUPG SCHEME

Abstract

This paper introduces ConvStabNet, a convolutional neural network that predicts optimal stabilization parameters for the Streamline Upwind Petrov Galerkin method (SUPG) stabilization scheme. To enhance the accuracy of SUPG in solving partial differential equations (PDE) with interior and bound- ary layers, ConvStabNet incorporates a loss function that combines a strong residual component and a cross-wind derivative term. ConvStabNet utilizes a shared parameter scheme, enabling the network to learn the correlations between cell properties and their respective stabilization parameters while effectively managing the parameter space. Comparative evaluations against state-of-the-art neural network solvers based on variational formulations demonstrate the superior performance of ConvStabNet. The results affirm ConvStabNet as a promising approach for accurately predicting stabilization parameters in SUPG, thereby establishing it as an improvement over neural network-based SUPG solvers