Two-level deep domain decomposition method
<|reference_start|>Two-level deep domain decomposition method: This study presents a two-level Deep Domain Decomposition Method (Deep-DDM) augmented with a coarse-level network for solving boundary value problems using physics-informed neural networks (PINNs). The addition of the coarse level network improves scalability and convergence rates compared to the single level method. Tested on a Poisson equation with Dirichlet boundary conditions, the two-level deep DDM demonstrates superior performance, maintaining efficient convergence regardless of the number of subdomains. This advance provides a more scalable and effective approach to solving complex partial differential equations with machine learning.<|reference_end|>
@article{dolean2024two-level,
    title={Two-level deep domain decomposition method},
    author={Victorita Dolean, Serge Gratton, Alexander Heinlein, Valentin Mercier},
    journal={arXiv preprint arXiv:2408.12198},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.12198},
    primaryClass={cs.LG cs.AI}
}