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：本文提出了一种新颖的数据驱动算子学习框架，称为随机先验小波神经算子（Randomized Prior Wavelet Neural Operator, RP-WNO）。该框架是近期提出的小波神经算子的扩展，后者虽具有卓越的泛化能力，却无法估计其预测结果的不确定性。与标准WNO不同，RP-WNO内置了不确定性量化模块，因此有望对科学家和工程师产生极大助益。RP-WNO采用随机先验网络，可整合先验信息，且相较于贝叶斯方法，更易于在大型复杂深度学习架构中实现。通过四个算例验证所提框架，结果表明该框架具有显著的有效性。