Conformalized-KANs：科学机器学习中Kolmogorov-Arnold网络（KANs）的具有覆盖保证的不确定性量化
Conformalized-KANs: Uncertainty Quantification with Coverage Guarantees for Kolmogorov-Arnold Networks (KANs) in Scientific Machine Learning
AI总结：
本文提出Conformalized-KANs，将保形预测与KAN集成结合，生成具有覆盖保证的校准预测区间，并在多种超参数设置下验证其鲁棒性，可扩展至FBKANs和MFKANs，提升科学机器学习中KANs的可靠性。
摘要：
本文探讨了Kolmogorov-Arnold网络（KANs）背景下的不确定性量化（UQ）方法。我们将集成方法应用于KANs，以获得启发式的UQ度量，增强复杂函数建模中的可解释性和鲁棒性。在此基础上，我们引入了Conformalized-KANs，该方法将无分布的不确定性量化技术——保形预测，与KAN集成相结合，以生成具有保证覆盖率的校准预测区间。我们进行了广泛的数值实验来评估这些方法的有效性，特别关注不同超参数设置下预测区间的鲁棒性和准确性。我们表明，保形KAN预测可应用于KANs的最新扩展，包括有限基KANs（FBKANs）和多保真度KANs（MFKANs）。结果表明，我们的方法有望提高KANs在科学机器学习中的可靠性和适用性。
英文摘要：
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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