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PINNfluence: Influence Functions for Physics-Informed Neural Networks

Authors :
Naujoks, Jonas R.
Krasowski, Aleksander
Weckbecker, Moritz
Wiegand, Thomas
Lapuschkin, Sebastian
Samek, Wojciech
Klausen, René P.
Publication Year :
2024

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.

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2409.08958
Document Type :
Working Paper