mlsanityData to 7 Oct 2026

Scalable Uncertainty Quantification for Deep Operator Networks using Randomized Priors

arXiv 2203.03048 ↗First posted 6 Mar 2022cs.LG stat.MLcited by 39

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Abstract (arXiv)

We present a simple and effective approach for posterior uncertainty quantification in deep operator networks (DeepONets); an emerging paradigm for supervised learning in function spaces. We adopt a frequentist approach based on randomized prior ensembles, and put forth an efficient vectorized implementation for fast parallel inference on accelerated hardware. Through a collection of representative examples in computational mechanics and climate modeling, we show that the merits of the proposed approach are fourfold. (1) It can provide more robust and accurate predictions when compared against deterministic DeepONets. (2) It shows great capability in providing reliable uncertainty estimates on scarce data-sets with multi-scale function pairs. (3) It can effectively detect out-of-distribution and adversarial examples. (4) It can seamlessly quantify uncertainty due to model bias, as well as noise corruption in the data. Finally, we provide an optimized JAX library called em UQDeepONet that can accommodate large model architectures, large ensemble sizes, as well as large data-sets with excellent parallel performance on accelerated hardware, thereby enabling uncertainty quantification for DeepONets in realistic large-scale applications.

Key facts. Cited by 39 papers in the map (data through 7 Oct 2026). Builds on 32 of its 69 references that are in the map. First posted on arXiv 6 Mar 2022.

Builds on

32 of 69 references.

References · 32

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2014Neural Machine Translation by Jointly Learning to Align and Translatecited by 4,530
  3. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,416
  4. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,888
  5. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  6. 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,597
  7. 2017What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?cited by 2,335
  8. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  9. 2018Averaging Weights Leads to Wider Optima and Better Generalizationcited by 1,194
  10. 2016Automatic chemical design using a data-driven continuous representation of moleculescited by 762
  11. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 722
  12. 2019A Simple Baseline for Bayesian Uncertainty in Deep Learningcited by 555
20 more
  1. 2015Weight Uncertainty in Neural Networkscited by 554
  2. 2017Solving high-dimensional partial differential equations using deep learningcited by 549
  3. 2016Deep Exploration via Bootstrapped DQNcited by 518
  4. 2019Deep Ensembles: A Loss Landscape Perspectivecited by 438
  5. 2021Neural Operator: Learning Maps Between Function Spacescited by 413
  6. 2020B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Datacited by 329
  7. 2015Scalable Bayesian Optimization Using Deep Neural Networkscited by 284
  8. 2020On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networkscited by 279
  9. 2018Randomized Prior Functions for Deep Reinforcement Learningcited by 218
  10. 2017Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equationscited by 208
  11. 2022Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisonscited by 169
  12. 2018Deep Bayesian Bandits Showdown: An Empirical Comparison of Bayesian Deep Networks for Thompson Samplingcited by 166
  13. 2018Adversarial Uncertainty Quantification in Physics-Informed Neural Networkscited by 120
  14. 2021Improved architectures and training algorithms for deep operator networkscited by 85
  15. 2018Quantifying Uncertainties in Natural Language Processing Taskscited by 79
  16. 2022DeepONet-Grid-UQ: A Trustworthy Deep Operator Framework for Predicting the Power Grid's Post-Fault Trajectoriescited by 30
  17. 2021Accelerated replica exchange stochastic gradient Langevin diffusion enhanced Bayesian DeepONet for solving noisy parametric PDEscited by 22
  18. 2018Physics-informed deep generative modelscited by 16
  19. 2021Output-Weighted Sampling for Multi-Armed Bandits with Extreme Payoffscited by 5
  20. 2019n-MeRCI: A new Metric to Evaluate the Correlation Between Predictive Uncertainty and True Errorcited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 5; 2023: 9; 2024: 10; 2025: 11; 2026: 4.

39 papers.

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  1. 2022Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transportcited by 92
  2. 2022Reliable extrapolation of deep neural operators informed by physics or sparse observationscited by 62
  3. 2022NeuralUQ: A comprehensive library for uncertainty quantification in neural differential equations and operatorscited by 33
  4. 2023Uncertainty quantification for noisy inputs-outputs in physics-informed neural networks and neural operatorscited by 28
  5. 2024RiemannONets: Interpretable Neural Operators for Riemann Problemscited by 28
  6. 2024Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networkscited by 28
  7. 2022Variationally Mimetic Operator Networkscited by 19
  8. 2023IB-UQ: Information bottleneck based uncertainty quantification for neural function regression and neural operator learningcited by 18
  9. 2023D2NO: Efficient Handling of Heterogeneous Input Function Spaces with Distributed Deep Neural Operatorscited by 18
  10. 2024Using Uncertainty Quantification to Characterize and Improve Out-of-Domain Learning for PDEscited by 14
  11. 2023On Approximating the Dynamic Response of Synchronous Generators via Operator Learning: A Step Towards Building Deep Operator-based Power Grid Simulatorscited by 13
  12. 2025Active operator learning with predictive uncertainty quantification for partial differential equationscited by 12
27 more
  1. 2022Variational Bayes Deep Operator Network: A data-driven Bayesian solver for parametric differential equationscited by 11
  2. 2024Composite Bayesian Optimization In Function Spaces Using NEON -- Neural Epistemic Operator Networkscited by 10
  3. 2024Federated scientific machine learning for approximating functions and solving differential equations with data heterogeneitycited by 8
  4. 2025Guaranteed prediction sets for functional surrogate modelscited by 7
  5. 2023A hybrid Decoder-DeepONet operator regression framework for unaligned observation datacited by 6
  6. 2024Time-Series Forecasting, Knowledge Distillation, and Refinement within a Multimodal PDE Foundation Modelcited by 6
  7. 2023Randomized prior wavelet neural operator for uncertainty quantificationcited by 4
  8. 2023Multi-fidelity climate model parameterization for better generalization and extrapolationcited by 4
  9. 2024Uncertainty quantification for deeponets with ensemble kalman inversioncited by 4
  10. 2024Alpha-VI DeepONet: A prior-robust variational Bayesian approach for enhancing DeepONets with uncertainty quantificationcited by 4
  11. 2025E-PINNs: Epistemic Physics-Informed Neural Networkscited by 4
  12. 2025Cauchy Random Features for Operator Learning in Sobolev Spacecited by 3
  13. 2025Conformalized-KANs: Uncertainty Quantification with Coverage Guarantees for Kolmogorov-Arnold Networks (KANs) in Scientific Machine Learningcited by 3
  14. 2023Scalable Bayesian optimization with high-dimensional outputs using randomized prior networkscited by 2
  15. 2024Learning Latent Space Dynamics with Model-Form Uncertainties: A Stochastic Reduced-Order Modeling Approachcited by 2
  16. 2024Empowering Bayesian Neural Networks with Functional Priors through Anchored Ensembling for Mechanics Surrogate Modeling Applicationscited by 2
  17. 2025Probabilistic Predictions of Process-Induced Deformation in Carbon/Epoxy Composites Using a Deep Operator Networkcited by 2
  18. 2025Towards Robust Surrogate Models: Benchmarking Machine Learning Approaches to Expediting Phase Field Simulations of Brittle Fracturecited by 1
  19. 2025LVM-GP: Uncertainty-Aware PDE Solver via coupling latent variable model and Gaussian processcited by 1
  20. 2025Deep set based operator learning with uncertainty quantificationcited by 1
  21. 2026Uncertainty-Aware Data-Based Method for Fast and Reliable Shape Optimizationcited by 1
  22. 2026Diffusion-Based Stochastic Operator Networks for Uncertainty Quantification in Stochastic Partial Differential Equationscited by 1
  23. 2026GeoQ: Geometry-Aware Conditional Quantile Error Estimation for Scientific Surrogate Modelscited by 1
  24. 2023Ensemble models outperform single model uncertainties and predictions for operator-learning of hypersonic flowscited by 0
  25. 2025An optimal Petrov-Galerkin framework for operator networkscited by 0
  26. 2025Active Learning Design: Modeling Force Output for Axisymmetric Soft Pneumatic Actuatorscited by 0
  27. 2026Two-Step MV-DeepONet: Probabilistic Operator Learning for Uncertainty Propagation Driven by Random Input Fieldscited by 0