Iterative Physics-Informed Neural Network for Solving Coupled Partial Differential Equations

The numerical solution of coupled partial differential equations (PDEs) represents a significant challenge for traditional methods such as the finite element method (FEM), particularly in the context of numerical stability and mesh generation. In this paper, an iterative physics-informed neural network (PINN) for solving coupled PDEs is proposed. The coupled PDEs are decomposed into a number of subproblems, which are then solved using multiple PINNs. An iterative method is proposed to update PINNs and reach convergence with coupled PDEs. The proposed method is capable of efficiently solving complex systems without the generation of fine meshes in the absence of data. The effectiveness and accuracy of the method are verified through an example of a coupled fluid dynamics and heat transfer example.