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

TL;DR

This paper introduces a distribution-free uncertainty quantification framework for Deep Operator Networks using conformal prediction, providing rigorous confidence intervals and improving uncertainty estimates across various numerical examples.

Contribution

The authors develop a novel split conformal prediction approach integrated with DeepONet variants, including a new Quantile-DeepONet, for effective uncertainty quantification.

Findings

Effective confidence intervals with coverage guarantees

Improved uncertainty quantification in PDE and multi-fidelity problems

Versatile framework applicable to various DeepONet architectures

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.