Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty
  Quantification in Deep Operator Networks
Christian Moya Amirhossein Mollaali Zecheng Zhang Lu Lu Guang Lin
In this paper, we adopt conformal prediction, a distribution-free uncertainty
quantification (UQ) framework, to obtain confidence prediction intervals with
coverage guarantees for Deep Operator Network (DeepONet) regression. Initially,
we enhance the uncertainty quantification frameworks (B-DeepONet and
Prob-DeepONet) previously proposed by the authors by using split conformal
prediction. By combining conformal prediction with our Prob- and B-DeepONets,
we effectively quantify uncertainty by generating rigorous confidence intervals
for DeepONet prediction. Additionally, we design a novel Quantile-DeepONet that
allows for a more natural use of split conformal prediction. We refer to this
distribution-free effective uncertainty quantification framework as split
conformal Quantile-DeepONet regression. Finally, we demonstrate the
effectiveness of the proposed methods using various ordinary, partial
differential equation numerical examples, and multi-fidelity learning.