Leveraging Influence Functions for Resampling Data in Physics-Informed Neural Networks

• URL: http://arxiv.org/abs/2506.16443v1
• Date: Thu, 19 Jun 2025 16:21:14 GMT
• Title: Leveraging Influence Functions for Resampling Data in Physics-Informed Neural Networks
• Authors: Jonas R. Naujoks, Aleksander Krasowski, Moritz Weckbecker, Galip Ümit Yolcu, Thomas Wiegand, Sebastian Lapuschkin, Wojciech Samek, René P. Klausen,
• Abstract summary: Physics-informed neural networks (PINNs) offer a powerful approach to solving partial differential equations (PDEs)<n>PINNs have recently emerged as a valuable tool in the field of scientific machine learning.
• Score: 45.752780408098765
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Physics-informed neural networks (PINNs) offer a powerful approach to solving partial differential equations (PDEs), which are ubiquitous in the quantitative sciences. Applied to both forward and inverse problems across various scientific domains, PINNs have recently emerged as a valuable tool in the field of scientific machine learning. A key aspect of their training is that the data -- spatio-temporal points sampled from the PDE's input domain -- are readily available. Influence functions, a tool from the field of explainable AI (XAI), approximate the effect of individual training points on the model, enhancing interpretability. In the present work, we explore the application of influence function-based sampling approaches for the training data. Our results indicate that such targeted resampling based on data attribution methods has the potential to enhance prediction accuracy in physics-informed neural networks, demonstrating a practical application of an XAI method in PINN training.

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