A machine learning approach to enhance the SUPG stabilization method for advection-dominated differential problems

<abstract><p>We propose using machine learning and artificial neural networks (ANNs) to enhance residual-based stabilization methods for advection-dominated differential problems. Specifically, in the context of finite element method, we consider streamline upwind Petrov-Galerkin (SUPG) method employ ANNs optimally choose parameter on which relies. We generate our dataset by solving optimization problems find optimal parameters that minimize distances among numerical exact solutions different data problem settings e.g., mesh size polynomial degree. The generated is used train ANN, latter "online" predict be SUPG any given setting data. show, means 1D 2D tests problem, ANN approach yields more accurate solution than conventional method.</p></abstract>