Efficient Physics Informed Neural Networks Coupled with Domain Decomposition Methods for Solving Coupled Multi-physics Problems

In this work, we introduce a novel coupled methodology called PINNs-DDM that combines a physics informed neural networks (PINNs) approach with a domain decomposition method (DDM) approach to solve multi-physics problems. The coupled methodology is applied to a variety of benchmark problems and validated against their exact solutions. Motivated by the need to solve coupled problems in enclosed spaces, we consider an application of coupling scalar transport equations to fluid dynamics equations using PINNs-DDM. While the examples and benchmark problems used in this work are in lower dimensions, they provide the necessary insight into the efficiency of the coupled method. It was noted that one of the key applications of the method is its performance for problems with limited training data. The computational results suggest that the method is very robust and can be applied to study complex real-world applications.