Uncertainty quantification for deeponets with ensemble kalman inversion

Andrew Pensoneault; Xueyu Zhu

doi:10.48550/arxiv.2403.03444

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Uncertainty quantification for deeponets with ensemble kalman inversion

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Uncertainty quantification for deeponets with ensemble kalman inversion

Andrew Pensoneault and Xueyu Zhu

arXiv.org

Cornell University

03/06/2024

DOI: 10.48550/arxiv.2403.03444

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Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

In recent years, operator learning, particularly the DeepONet, has received much attention for efficiently learning complex mappings between input and output functions across diverse fields. However, in practical scenarios with limited and noisy data, accessing the uncertainty in DeepONet predictions becomes essential, especially in mission-critical or safety-critical applications. Existing methods, either computationally intensive or yielding unsatisfactory uncertainty quantification, leave room for developing efficient and informative uncertainty quantification (UQ) techniques tailored for DeepONets. In this work, we proposed a novel inference approach for efficient UQ for operator learning by harnessing the power of the Ensemble Kalman Inversion (EKI) approach. EKI, known for its derivative-free, noise-robust, and highly parallelizable feature, has demonstrated its advantages for UQ for physics-informed neural networks [28]. Our innovative application of EKI enables us to efficiently train ensembles of DeepONets while obtaining informative uncertainty estimates for the output of interest. We deploy a mini-batch variant of EKI to accommodate larger datasets, mitigating the computational demand due to large datasets during the training stage. Furthermore, we introduce a heuristic method to estimate the artificial dynamics covariance, thereby improving our uncertainty estimates. Finally, we demonstrate the effectiveness and versatility of our proposed methodology across various benchmark problems, showcasing its potential to address the pressing challenges of uncertainty quantification in DeepONets, especially for practical applications with limited and noisy data.

Computer Science - Artificial Intelligence

Computer Science - Learning

Computer Science - Numerical Analysis

Mathematics - Numerical Analysis

Statistics - Machine Learning

Details

Title: Subtitle: Uncertainty quantification for deeponets with ensemble kalman inversion
Creators: Andrew Pensoneault
Xueyu Zhu
Resource Type: Preprint
Publication Details: arXiv.org
Publisher: Cornell University; Ithaca, New York
DOI: 10.48550/arxiv.2403.03444
eISSN: 2331-8422
Language: English
Date posted: 03/06/2024
Academic Unit: IIHR--Hydroscience and Engineering; Mathematics
Record Identifier: 9984573560302771

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