PINNfluence: Influence Functions for Physics-Informed Neural Networks
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.
Cite
@article{arxiv.2409.08958,
title = {PINNfluence: Influence Functions for Physics-Informed Neural Networks},
author = {Jonas R. Naujoks and Aleksander Krasowski and Moritz Weckbecker and Thomas Wiegand and Sebastian Lapuschkin and Wojciech Samek and René P. Klausen},
journal= {arXiv preprint arXiv:2409.08958},
year = {2024}
}