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

Influence functions can improve AI accuracy in scientific computing: The paper demonstrates that using influence functions—a tool that identifies which training data points matter most—can enhance the prediction accuracy of physics-informed neural networks (PINNs) when solving complex mathematical equations used across science and engineering.

Explainability methods have practical benefits beyond transparency: Rather than serving only to explain AI decisions after the fact, influence functions from explainable AI (XAI) can be actively used during training to strategically resample data, showing that interpretability tools can directly improve model performance.

Targeted data selection beats random sampling: The research suggests that intelligently choosing which training data points to use—based on their individual influence on the model—is more effective than randomly sampling data points, potentially reducing computational costs while maintaining or improving accuracy.

This approach applies to real-world scientific problems: PINNs are used to solve partial differential equations across quantitative sciences, meaning this influence function-based resampling technique could have practical applications in physics, engineering, climate modeling, and other domains where these equations are fundamental.