Randomized prior wavelet neural operator for uncertainty quantification

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.