FB-HyDON: Parameter-Efficient Physics-Informed Operator Learning of Complex PDEs via Hypernetwork and Finite Basis Domain Decomposition
<|reference_start|>FB-HyDON: Parameter-Efficient Physics-Informed Operator Learning of Complex PDEs via Hypernetwork and Finite Basis Domain Decomposition: Deep operator networks (DeepONet) and neural operators have gained significant attention for their ability to map infinite-dimensional function spaces and perform zero-shot super-resolution. However, these models often require large datasets for effective training. While physics-informed operators offer a data-agnostic learning approach, they introduce additional training complexities and convergence issues, especially in highly nonlinear systems. To overcome these challenges, we introduce Finite Basis Physics-Informed HyperDeepONet (FB-HyDON), an advanced operator architecture featuring intrinsic domain decomposition. By leveraging hypernetworks and finite basis functions, FB-HyDON effectively mitigates the training limitations associated with existing physics-informed operator learning methods. We validated our approach on the high-frequency harmonic oscillator, Burgers' equation at different viscosity levels, and Allen-Cahn equation demonstrating substantial improvements over other operator learning models.<|reference_end|>
@article{ramezankhani2024fb-hydon:,
    title={FB-HyDON: Parameter-Efficient Physics-Informed Operator Learning of
  Complex PDEs via Hypernetwork and Finite Basis Domain Decomposition},
    author={Milad Ramezankhani, Rishi Yash Parekh, Anirudh Deodhar, Dagnachew
  Birru},
    journal={arXiv preprint arXiv:2409.09207},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.09207},
    primaryClass={cs.LG cs.NA math.NA physics.app-ph}
}