  An artificial intelligence-augmented Streamline Upwind/Petrov-Galerkin finite
element scheme (AiStab-FEM) is proposed for solving singularly perturbed
partial differential equations. In particular, an artificial neural network
framework is proposed to predict optimal values for the stabilization
parameter. The neural network is trained by minimizing a physics-informed cost
function, where the equation's mesh and physical parameters are used as input
features. Further, the predicted stabilization parameter is normalized with the
gradient of the Galerkin solution to treat the boundary/interior layer region
adequately. The proposed approach suppresses the undershoots and overshoots in
the stabilized finite element solution and outperforms the existing neural
network-based partial differential equation solvers such as Physics-Informed
Neural Networks and Variational Neural Networks.
