Coupling of the Finite Element Method with Physics Informed Neural Networks for the Multi-Fluid Flow Problem
<|reference_start|>Coupling of the Finite Element Method with Physics Informed Neural Networks for the Multi-Fluid Flow Problem: Multi-fluid flows are found in various industrial processes, including metal injection molding and 3D printing. The accuracy of multi-fluid flow modeling is determined by how well interfaces and capillary forces are represented. In this paper, the multi-fluid flow problem is discretized using a combination of a Physics-Informed Neural Network (PINN) with a finite element discretization. To determine the best PINN formulation, a comparative study is conducted using a manufactured solution. We compare interface reinitialization methods to determine the most suitable approach for our discretization strategy. We devise a neural network architecture that better handles complex free surface topologies. Finally, the coupled numerical strategy is used to model a rising bubble problem.<|reference_end|>
@article{nohra2024coupling,
    title={Coupling of the Finite Element Method with Physics Informed Neural
  Networks for the Multi-Fluid Flow Problem},
    author={Michel Nohra, Steven Dufour},
    journal={arXiv preprint arXiv:2405.05371},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.05371},
    primaryClass={math.NA cs.NA}
}