Before revision:  We show how to integrate PINN with traditional scientific computing approaches , such as multigrid and Gauss-Seidel methods. While the accuracy and computational performance is still a limiting factor for the direct use of PINN for solving , hybrid strategies are a viable option for the development of a new class of linear solvers combining emerging deep-learning and traditional scientific computing approaches .
After revision:  We show how to integrate PINN with traditional scientific computing approaches , such as PETSc conjugate gradient linear solvers, in terms of performance and accuracy. Overall, while the accuracy and computational performance is still a limiting factor for the direct use of PINN for solving , hybrid strategies are a viable option for the development of a new class of linear solvers combining emerging deep-learning and traditional scientific computing approaches .