Randomized prior wavelet neural operator for uncertainty quantification
This work addresses the need for uncertainty quantification in data-driven operator learning for scientists and engineers, offering an incremental improvement over existing methods.
The authors tackled the problem of uncertainty quantification in operator learning by extending the wavelet neural operator with randomized prior networks, resulting in a framework that provides inherent uncertainty estimates and is easier to implement than Bayesian methods, as demonstrated through four solved examples.
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.