PINNfluence: Influence Functions for Physics-Informed Neural Networks
<|reference_start|>PINNfluence: Influence Functions for Physics-Informed Neural Networks: Recently, physics-informed neural networks (PINNs) have emerged as a flexible and promising application of deep learning to partial differential equations in the physical sciences. While offering strong performance and competitive inference speeds on forward and inverse problems, their black-box nature limits interpretability, particularly regarding alignment with expected physical behavior. In the present work, we explore the application of influence functions (IFs) to validate and debug PINNs post-hoc. Specifically, we apply variations of IF-based indicators to gauge the influence of different types of collocation points on the prediction of PINNs applied to a 2D Navier-Stokes fluid flow problem. Our results demonstrate how IFs can be adapted to PINNs to reveal the potential for further studies.<|reference_end|>
@article{naujoks2024pinnfluence:,
    title={PINNfluence: Influence Functions for Physics-Informed Neural Networks},
    author={Jonas R. Naujoks, Aleksander Krasowski, Moritz Weckbecker, Thomas
  Wiegand, Sebastian Lapuschkin, Wojciech Samek, Ren'e P. Klausen},
    journal={arXiv preprint arXiv:2409.08958},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.08958},
    primaryClass={cs.LG cs.AI physics.comp-ph physics.flu-dyn}
}