mlsanityData to 14 Oct 2026

Alpha-VI DeepONet: A prior-robust variational Bayesian approach for enhancing DeepONets with uncertainty quantification

arXiv 2408.00681 ↗First posted 1 Aug 2024stat.ML cs.LGcited by 4

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Abstract (arXiv)

We introduce a novel deep operator network (DeepONet) framework that incorporates generalised variational inference (GVI) using R'enyi's α-divergence to learn complex operators while quantifying uncertainty. By incorporating Bayesian neural networks as the building blocks for the branch and trunk networks, our framework endows DeepONet with uncertainty quantification. The use of R'enyi's α-divergence, instead of the Kullback-Leibler divergence (KLD), commonly used in standard variational inference, mitigates issues related to prior misspecification that are prevalent in Variational Bayesian DeepONets. This approach offers enhanced flexibility and robustness. We demonstrate that modifying the variational objective function yields superior results in terms of minimising the mean squared error and improving the negative log-likelihood on the test set. Our framework's efficacy is validated across various mechanical systems, where it outperforms both deterministic and standard KLD-based VI DeepONets in predictive accuracy and uncertainty quantification. The hyperparameter α, which controls the degree of robustness, can be tuned to optimise performance for specific problems. We apply this approach to a range of mechanics problems, including gravity pendulum, advection-diffusion, and diffusion-reaction systems. Our findings underscore the potential of α-VI DeepONet to advance the field of data-driven operator learning and its applications in engineering and scientific domains.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 31 of its 56 references that are in the map. First posted on arXiv 1 Aug 2024.

Builds on

31 of 56 references.

References · 31

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
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  5. 2022FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operatorscited by 776
  6. 2015Variational Dropout and the Local Reparameterization Trickcited by 490
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  10. 2022Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisonscited by 170
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  12. 2021Bayesian Neural Network Priors Revisitedcited by 121
19 more
  1. 2022Physics-Informed Deep Neural Operator Networkscited by 113
  2. 2017TensorFlow Distributionscited by 106
  3. 2016R'enyi Divergence Variational Inferencecited by 104
  4. 2017Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inferencecited by 98
  5. 2021A physics-informed variational DeepONet for predicting the crack path in brittle materialscited by 98
  6. 2022Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transportcited by 92
  7. 2023Kernel Methods are Competitive for Operator Learningcited by 50
  8. 2022Scalable Uncertainty Quantification for Deep Operator Networks using Randomized Priorscited by 39
  9. 2023Novel DeepONet architecture to predict stresses in elastoplastic structures with variable complex geometries and loadscited by 33
  10. 2024Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networkscited by 28
  11. 2022Bi-fidelity Modeling of Uncertain and Partially Unknown Systems using DeepONetscited by 27
  12. 2019Expressive Priors in Bayesian Neural Networks: Kernel Combinations and Periodic Functionscited by 22
  13. 2021Accelerated replica exchange stochastic gradient Langevin diffusion enhanced Bayesian DeepONet for solving noisy parametric PDEscited by 22
  14. 2018Doubly Robust Bayesian Inference for Non-Stationary Streaming Data with β-Divergencescited by 21
  15. 2023IB-UQ: Information bottleneck based uncertainty quantification for neural function regression and neural operator learningcited by 18
  16. 2023A DeepONet multi-fidelity approach for residual learning in reduced order modelingcited by 14
  17. 2023A multi-fidelity deep operator network (DeepONet) for fusing simulation and monitoring data: Application to real-time settlement prediction during tunnel constructioncited by 12
  18. 2021Generalized Joint Probability Density Function Formulation inTurbulent Combustion using DeepONetcited by 8
  19. 2024Uncertainty quantification for deeponets with ensemble kalman inversioncited by 4

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 0; 2026: 3.

4 papers.

  1. 2024Towards Gaussian Process for operator learning: an uncertainty aware resolution independent operator learning algorithm for computational mechanicscited by 3
  2. 2026pADAM: A Plug-and-Play All-in-One Diffusion Architecture for Multi-Physics Learningcited by 0
  3. 2026PGD-NO: A Neural Operator with Precomputed Geometry Decomposition for 3D Million-scale Physics Simulationscited by 0
  4. 2026Two-Step MV-DeepONet: Probabilistic Operator Learning for Uncertainty Propagation Driven by Random Input Fieldscited by 0