In this paper, we propose a novel data-driven operator learning framework referred to as the \textit{Randomized Prior Wavelet Neural Operator} (RP-WNO). The proposed RP-WNO is an extension of the recently proposed wavelet neural operator, which boasts excellent generalizing capabilities but cannot estimate the uncertainty associated with its predictions. RP-WNO, unlike the vanilla WNO, comes with inherent uncertainty quantification module and hence, is expected to be extremely useful for scientists and engineers alike. RP-WNO utilizes randomized prior networks, which can account for prior information and is easier to implement for large, complex deep-learning architectures than its Bayesian counterpart. Four examples have been solved to test the proposed framework, and the results produced advocate favorably for the efficacy of the proposed framework.

翻译：在本文中,我们提出了一个新的数据驱动操作员学习框架,称为“RP-WNO ” ( RP-WNO ) 。 拟议的RP-WNO是最近提议的波子神经操作员的延伸,该操作员拥有极好的概括性能力,但无法估计与预测相关的不确定性。 RP-WNO与Vanilla WNO不同,具有内在的不确定性量化模块,因此预计对科学家和工程师都极为有用。 RP-WNO利用随机化的先前网络,这些网络可以说明先前的信息,并且较之其巴伊西亚对应方更容易实施大型的、复杂的深层学习架构。 解决了四个例子来测试拟议的框架,并积极倡导拟议框架的有效性。