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.

翻译：本文采用共形预测这一无分布的不确定性量化框架，为深度算子网络回归获得具有覆盖保证的置信预测区间。首先，我们通过使用分割共形预测，改进了作者先前提出的不确定性量化框架（B-DeepONet和Prob-DeepONet）。通过将共形预测与我们的Prob-和B-DeepONets相结合，我们有效生成了DeepONet预测的严格置信区间，从而量化不确定性。此外，我们设计了一种新颖的Quantile-DeepONet，使得分割共形预测的应用更为自然。我们将这种无分布的有效不确定性量化框架称为分割共形Quantile-DeepONet回归。最后，通过多种常微分方程、偏微分方程数值算例及多保真度学习，验证了所提方法的有效性。