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

翻译：我们首次在Kolmogorov-Arnold Networks领域引入了不确定性量化方法，特别聚焦于（高阶）ReLUKANs，以提升贝叶斯方法在计算需求下的计算效率。所提出的方法具有通用性，能够同时获取认知不确定性和偶然不确定性，并可推广至其他各类基函数。我们通过一系列闭合测试验证了该方法，包括简单的一维函数测试以及在（随机）偏微分方程领域的应用。针对后者，我们证明了该方法能够正确识别通过引入随机项所产生的函数依赖关系。本工作的支持代码可在https://github.com/wmdataphys/Bayesian-HR-KAN 获取。