Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networks
<|reference_start|>Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networks: 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.<|reference_end|>
@article{moya2024conformalized-deeponet:,
    title={Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty
  Quantification in Deep Operator Networks},
    author={Christian Moya, Amirhossein Mollaali, Zecheng Zhang, Lu Lu, Guang Lin},
    journal={arXiv preprint arXiv:2402.15406},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.15406},
    primaryClass={cs.LG cs.NA math.NA}
}