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

TL;DR

This paper explores using influence functions from explainable AI to selectively resample training data in physics-informed neural networks, aiming to improve their prediction accuracy in solving PDEs.

Contribution

It introduces a novel application of influence functions for data resampling in PINNs, enhancing their training process and predictive performance.

Findings

Influence function-based resampling improves PINN accuracy

Targeted data selection enhances model interpretability

Demonstrates practical use of XAI methods in scientific ML

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.