PINNfluence: Influence Functions for Physics-Informed Neural Networks
This work addresses interpretability issues for researchers using PINNs in physical sciences, but it is incremental as it adapts existing influence function techniques to a specific domain.
The authors tackled the lack of interpretability in physics-informed neural networks (PINNs) by applying influence functions to analyze how collocation points affect predictions in a 2D Navier-Stokes fluid flow problem, demonstrating the method's potential for validation and debugging.
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.