PINNfluence: Influence Functions for Physics-Informed Neural Networks

• URL: http://arxiv.org/abs/2409.08958v2
• Date: Sun, 01 Dec 2024 06:47:45 GMT
• Title: PINNfluence: Influence Functions for Physics-Informed Neural Networks
• Authors: Jonas R. Naujoks, Aleksander Krasowski, Moritz Weckbecker, Thomas Wiegand, Sebastian Lapuschkin, Wojciech Samek, René P. Klausen,
• Abstract summary: Physics-informed neural networks (PINNs) have emerged as a flexible and promising application of deep learning to partial differential equations in the physical sciences. We explore the application of influence functions (IFs) to validate and debug PINNs post-hoc.
• Score: 47.27512105490682
• License:
• Abstract: 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.

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