Coupling PIES and PINN for Solving Two-Dimensional Boundary Value Problems via Domain Decomposition

The paper proposes coupling Parametric Integral Equation System (PIES) and Physics-Informed Neural Network (PINN) for solving two-dimensional potential boundary value problems defined by the Laplace equation. As a result, the computational domain can be decomposed into subdomains, where solutions are obtained independently using PIES and PINN while simultaneously satisfying interface connection conditions. The efficacy of this approach is validated through a numerical example.