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[2503.03178] Active operator learning with predictive uncertainty quantification for partial differential equations
Summary
The paper presents a lightweight predictive uncertainty quantification method for neural operators in solving partial differential equations, enhancing accuracy and efficiency in scientific applications.
Why It Matters
As neural operators become more prevalent in solving partial differential equations (PDEs), understanding their predictive accuracy and uncertainty is crucial for reliable deployment in scientific contexts. This research addresses the computational challenges of existing uncertainty quantification methods, providing a faster and more efficient alternative that can significantly improve data efficiency and accuracy in real-time applications.
Key Takeaways
- Proposes a lightweight predictive uncertainty quantification method for neural operators.
- Demonstrates unbiased uncertainty estimates and accurate out-of-distribution predictions.
- Offers significant speed improvements in inference times, reducing evaluation by over five times.
- Extends the framework to Fourier Neural Operators and other operator networks.
- Highlights the application of predictive uncertainties in Bayesian optimization and active learning.
Computer Science > Machine Learning arXiv:2503.03178 (cs) [Submitted on 5 Mar 2025 (v1), last revised 25 Feb 2026 (this version, v4)] Title:Active operator learning with predictive uncertainty quantification for partial differential equations Authors:Nick Winovich, Mitchell Daneker, Lu Lu, Guang Lin View a PDF of the paper titled Active operator learning with predictive uncertainty quantification for partial differential equations, by Nick Winovich and 3 other authors View PDF HTML (experimental) Abstract:With the increased prevalence of neural operators being used to provide rapid solutions to partial differential equations (PDEs), understanding the accuracy of model predictions and the associated error levels is necessary for deploying reliable surrogate models in scientific applications. Existing uncertainty quantification (UQ) frameworks employ ensembles or Bayesian methods, which can incur substantial computational costs during both training and inference. We propose a lightweight predictive UQ method tailored for Deep operator networks (DeepONets) that also generalizes to other operator networks. Numerical experiments on linear and nonlinear PDEs demonstrate that the framework's uncertainty estimates are unbiased and provide accurate out-of-distribution uncertainty predictions with a sufficiently large training dataset. Our framework provides fast inference and uncertainty estimates that can efficiently drive outer-loop analyses that would be prohibitively expensive ...
