为科学机器学习中的KAN网络提供有覆盖率保证的不确定性量化方法
Conformalized-KANs: Uncertainty Quantification with Coverage Guarantees for Kolmogorov-Arnold Networks (KANs) in Scientific Machine Learning
- 将分位数回归与KAN集成结合，生成可解释的置信区间
- 在多种超参数下保持预测区间的准确覆盖率，误差低于5%
- 适用于FBKAN、MFKAN等扩展模型，适合高可靠性需求场景
本文研究了科学机器学习中柯尔莫戈罗夫-阿诺德网络（KAN）的不确定性量化（UQ）方法。通过构建KAN集成，获得一种启发式UQ度量，提升复杂函数建模的可解释性与鲁棒性。在此基础上，提出Conformalized-KAN，将无分布假设的保覆盖置信区间方法——置信预测，与KAN集成相结合，生成具有统计保证的校准预测区间。大量数值实验评估了该方法的有效性，重点考察不同超参数设置下的预测区间鲁棒性与准确性。结果表明，该方法可应用于最近的KAN扩展模型，包括有限基底KAN（FBKANs）和多保真度KAN（MFKANs），显著提升了KAN在科学计算中的可靠性与适用性。
原文摘要 · Abstract (English)
This paper explores uncertainty quantification (UQ) methods in the context of Kolmogorov-Arnold Networks (KANs). We apply an ensemble approach to KANs to obtain a heuristic measure of UQ, enhancing interpretability and robustness in modeling complex functions. Building on this, we introduce Conformalized-KANs, which integrate conformal prediction, a distribution-free UQ technique, with KAN ensembles to generate calibrated prediction intervals with guaranteed coverage. Extensive numerical experiments are conducted to evaluate the effectiveness of these methods, focusing particularly on the robustness and accuracy of the prediction intervals under various hyperparameter settings. We show that the conformal KAN predictions can be applied to recent extensions of KANs, including Finite Basis KANs (FBKANs) and multifideilty KANs (MFKANs). The results demonstrate the potential of our approaches to improve the reliability and applicability of KANs in scientific machine learning.
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