Before revision:  We test and evaluate PINN performance under different  configurations (depth, activation functions, input data set distribution , and transfer learningimpact). We show how to integrate PINN with traditional scientific computing approaches , such as multigrid and Gauss-Seidel methods.
After revision:  We test and evaluate PINN performance under different configurations (depth, activation functions, input data set distribution ). We highlight the critical role of transfer learning. Our results show that low-frequency components of the solution converge quickly as an effect of the F-principle. In contrast, an accurate solution of the high frequencies requires an exceedingly long time. To address this limitation, we propose integrating PINNs into traditional linear solvers. We show that this integration leads to the development of new solvers whose performance is on par with other high-performance solvers , such as multigrid and Gauss-Seidel methods.