首个面向高阶ReLU KAN的不确定性量化方法，兼顾效率与精度。
Uncertainty Quantification with Bayesian Higher Order ReLU KANs
- 基于贝叶斯框架构建高阶ReLU KAN，实现高效不确定性估计。
- 可同时捕捉认知不确定性和随机不确定性，在1D函数与随机偏微分方程上验证有效。
- 适用于多种基函数，适合需可信预测的科学计算场景。
我们提出首个针对科尔莫戈罗夫-阿诺德网络（Kolmogorov-Arnold Networks）的不确定性量化方法，聚焦于（高阶）ReLU KAN，以应对贝叶斯方法的计算开销问题。该方法具有通用性，可同时获取认知不确定性与随机不确定性，并能推广至其他基函数。通过一系列闭合测试验证，包括一维函数及（随机）偏微分方程的应用。在后者中，方法成功识别出引入随机项所导致的函数依赖关系。代码已开源：https://github.com/wmdataphys/Bayesian-HR-KAN。
原文摘要 · Abstract (English)
We introduce the first method of uncertainty quantification in the domain of Kolmogorov-Arnold Networks, specifically focusing on (Higher Order) ReLUKANs to enhance computational efficiency given the computational demands of Bayesian methods. The method we propose is general in nature, providing access to both epistemic and aleatoric uncertainties. It is also capable of generalization to other various basis functions. We validate our method through a series of closure tests, including simple one-dimensional functions and application to the domain of (Stochastic) Partial Differential Equations. Referring to the latter, we demonstrate the method's ability to correctly identify functional dependencies introduced through the inclusion of a stochastic term. The code supporting this work can be found at https://github.com/wmdataphys/Bayesian-HR-KAN
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