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.

采用符合预测方法的分布自由不确定性量化框架，获得具有覆盖保证的深度操作网络回归的置信度预测区间，并通过将符合预测与Prob-DeepONet和B-DeepONet相结合，有效地量化不确定性，生成严谨的深度操作网络预测的置信度区间，同时设计一种新颖的Quantile-DeepONet，允许更自然地使用符合预测，被称为符合预测的Quantile-DeepONet回归的无分布有效不确定性量化框架，并通过各种常规、偏微分方程数值示例和多保真度学习证明所提出方法的有效性。

Conformalized-DeepONet：深度操作器网络中的无分布框架不确定性量化