mlsanityData to 7 Oct 2026

Deep Operator Learning-based Surrogate Models with Uncertainty Quantification for Optimizing Internal Cooling Channel Rib Profiles

arXiv 2306.00810 ↗First posted 1 Jun 2023physics.flu-dyn cs.LG cs.NAcited by 10

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Abstract (arXiv)

This paper designs surrogate models with uncertainty quantification capabilities to improve the thermal performance of rib-turbulated internal cooling channels effectively. To construct the surrogate, we use the deep operator network (DeepONet) framework, a novel class of neural networks designed to approximate mappings between infinite-dimensional spaces using relatively small datasets. The proposed DeepONet takes an arbitrary continuous rib geometry with control points as input and outputs continuous detailed information about the distribution of pressure and heat transfer around the profiled ribs. The datasets needed to train and test the proposed DeepONet framework were obtained by simulating a 2D rib-roughened internal cooling channel. To accomplish this, we continuously modified the input rib geometry by adjusting the control points according to a simple random distribution with constraints, rather than following a predefined path or sampling method. The studied channel has a hydraulic diameter, Dh, of 66.7 mm, and a length-to-hydraulic diameter ratio, L/Dh, of 10. The ratio of rib center height to hydraulic diameter (e/Dh), which was not changed during the rib profile update, was maintained at a constant value of 0.048. The ribs were placed in the channel with a pitch-to-height ratio (P/e) of 10. In addition, we provide the proposed surrogates with effective uncertainty quantification capabilities. This is achieved by converting the DeepONet framework into a Bayesian DeepONet (B-DeepONet). B-DeepONet samples from the posterior distribution of DeepONet parameters using the novel framework of stochastic gradient replica-exchange MCMC.

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Builds on 6 of its 35 references that are in the map. First posted on arXiv 1 Jun 2023.

Builds on

6 of 35 references.

References · 6

  1. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  2. 2022Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisonscited by 169
  3. 2022Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transportcited by 92
  4. 2020Non-convex Learning via Replica Exchange Stochastic Gradient MCMCcited by 33
  5. 2022DeepONet-Grid-UQ: A Trustworthy Deep Operator Framework for Predicting the Power Grid's Post-Fault Trajectoriescited by 30
  6. 2022DeepGraphONet: A Deep Graph Operator Network to Learn and Zero-shot Transfer the Dynamic Response of Networked Systemscited by 14

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 3; 2025: 2; 2026: 2.

10 papers.

  1. 2024Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networkscited by 28
  2. 2023D2NO: Efficient Handling of Heterogeneous Input Function Spaces with Distributed Deep Neural Operatorscited by 18
  3. 2024Point-DeepONet: Predicting Nonlinear Fields on Non-Parametric Geometries under Variable Load Conditionscited by 10
  4. 2024Conformalized Prediction of Post-Fault Voltage Trajectories Using Pre-trained and Finetuned Attention-Driven Neural Operatorscited by 5
  5. 2023A Physics-Guided Bi-Fidelity Fourier-Featured Operator Learning Framework for Predicting Time Evolution of Drag and Lift Coefficientscited by 4
  6. 2025Conformalized-KANs: Uncertainty Quantification with Coverage Guarantees for Kolmogorov-Arnold Networks (KANs) in Scientific Machine Learningcited by 3
  7. 2025Single vs. Multiple Branches in DeepONet and S-DeepONet: Network Architecture Follows Coupling in Multiphysics Systemscited by 2
  8. 2023B-LSTM-MIONet: Bayesian LSTM-based Neural Operators for Learning the Response of Complex Dynamical Systems to Length-Variant Multiple Input Functionscited by 1
  9. 2026Distribution-Free Robust Predict-Then-Optimize in Function Spacescited by 0
  10. 2026Two-Step MV-DeepONet: Probabilistic Operator Learning for Uncertainty Propagation Driven by Random Input Fieldscited by 0