This study examines the efficacy of Physics Informed Neural Networks with a domain-distributed architecture (DPINN) in solving two-phase flow benchmark problems. Focusing on an unsteady, incompressible scenario, our DPINN framework utilizes a Volume of Fluid (VOF) approach for accurate simulation of interface dynamics. Training data, incorporating interface position information, refines the domain proximal to the interface. Validation against a CFD-based model establishes the accuracy of the PINN model without domain distribution.
The study advances to a Distributed Physics Informed Neural Network (DPINN) architecture, partitioning the global domain into non-overlapping sub-domains. Solutions from each subdomain are linked using interface conditions in the loss function. Additionally, a Transfer PINN (TPINN) architecture is explored, which has multiple shared layers and at least one layer with unique parameters. The investigation covers parameters influencing the distributed PINN architecture, including sub-domain width, loss term weights, and local network size. Network parameters such as training batch size and learning-rate scheduling are also considered. Significantly, the study highlights the dynamic adjustment of weights in the DPINN loss function. Initially assigned manually, a self-adaptive weighting strategy based on the Gaussian probabilistic model is introduced, ensuring balanced convergence of different loss terms.