A Generalized Schwarz-type Non-overlapping Domain Decomposition Method using Physics-constrained Neural Networks

Understand

We present a meshless Schwarz-type non-overlapping domain decomposition method based on artificial neural networks for solving forward and inverse problems involving partial differential equations (PDEs).

• To ensure the consistency of solutions across neighboring subdomains, we adopt a generalized Robin-type interface condition, assigning unique Robin parameters to each subdomain.
• These subdomain-specific Robin parameters are learned to minimize the mismatch on the Robin interface condition, facilitating efficient information exchange during training.
• Our method is applicable to both the Laplace's and Helmholtz equations.