Petrov-Galerkin Variational Physics-Informed Neural Network Framework for Two-Dimensional Singularly Perturbed Problems
Researchers have developed a new Petrov-Galerkin Variational Physics-Informed Neural Network (VPINN) framework designed to efficiently solve complex two-dimensional problems with small perturbation parameters. This method utilizes neural networks for trial solutions and tensor-product hat functions as test functions, incorporating a Petrov-Galerkin formulation to accurately capture sharp boundary layers. Computational tests indicate that the proposed VPINN approach achieves high accuracy and demonstrates robustness in handling the multiscale features of these problems. AI