Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networks

• URL: http://arxiv.org/abs/2402.15406v1
• Date: Fri, 23 Feb 2024 16:07:39 GMT
• Title: Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networks
• Authors: Christian Moya, Amirhossein Mollaali, Zecheng Zhang, Lu Lu, Guang Lin
• Abstract summary: We use conformal prediction to obtain confidence prediction intervals with coverage guarantees for Deep Operator Network (DeepONet) regression. We design a novel Quantile-DeepONet that allows for a more natural use of split conformal prediction. We demonstrate the effectiveness of the proposed methods using various ordinary, partial differential equation numerical examples.
• Score: 7.119066725173193
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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