用可解释AI方法重采样数据，提升物理神经网络的预测精度。
Leveraging Influence Functions for Resampling Data in Physics-Informed Neural Networks
- 基于影响函数筛选关键训练点进行重采样
- 实验显示能有效提高物理信息神经网络的预测准确率
- 适合关注模型可解释性与训练优化的研究者
物理信息神经网络（PINNs）为求解偏微分方程（PDEs）提供了强大工具，广泛应用于正向与逆向问题。其训练依赖于从PDE定义域中采样的时空数据点，这些数据点易于获取。影响函数是可解释人工智能（XAI）中的工具，用于近似单个训练样本对模型的影响，增强模型可解释性。本文探索将基于影响函数的采样方法应用于PINN的训练数据。结果表明，基于数据归因的靶向重采样具有提升PINN预测精度的潜力，展示了XAI方法在PINN训练中的实用价值。
原文摘要 · Abstract (English)
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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