Leveraging Influence Functions for Resampling Data in Physics-Informed Neural Networks
This work addresses training efficiency for PINN users in scientific machine learning, but appears incremental as it applies an existing XAI method to a new context.
The authors tackled the problem of improving prediction accuracy in Physics-Informed Neural Networks (PINNs) by applying influence function-based resampling to training data, demonstrating its potential as a practical XAI application in PINN training.
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.