Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networks
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916135978401792 |
|---|---|
| author | Moya, Christian Mollaali, Amirhossein Zhang, Zecheng Lu, Lu Lin, Guang |
| author_facet | Moya, Christian Mollaali, Amirhossein Zhang, Zecheng Lu, Lu Lin, Guang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15406 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networks Moya, Christian Mollaali, Amirhossein Zhang, Zecheng Lu, Lu Lin, Guang Machine Learning Numerical Analysis 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. |
| title | Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networks |
| topic | Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2402.15406 |