PINNfluence: Influence Functions for Physics-Informed Neural Networks
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913591826841600 |
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| author | Naujoks, Jonas R. Krasowski, Aleksander Weckbecker, Moritz Wiegand, Thomas Lapuschkin, Sebastian Samek, Wojciech Klausen, René P. |
| author_facet | Naujoks, Jonas R. Krasowski, Aleksander Weckbecker, Moritz Wiegand, Thomas Lapuschkin, Sebastian Samek, Wojciech Klausen, René P. |
| contents | 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. The code is publicly available at https://github.com/aleks-krasowski/PINNfluence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08958 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | PINNfluence: Influence Functions for Physics-Informed Neural Networks Naujoks, Jonas R. Krasowski, Aleksander Weckbecker, Moritz Wiegand, Thomas Lapuschkin, Sebastian Samek, Wojciech Klausen, René P. Machine Learning Artificial Intelligence Computational Physics Fluid Dynamics 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. The code is publicly available at https://github.com/aleks-krasowski/PINNfluence. |
| title | PINNfluence: Influence Functions for Physics-Informed Neural Networks |
| topic | Machine Learning Artificial Intelligence Computational Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2409.08958 |