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This paper designs surrogate models with uncertainty quantificationcapabilities to improve the thermal performance of rib-turbulated internalcooling channels effectively. To construct the surrogate, we use the deepoperator network (DeepONet) framework, a novel class of neural networksdesigned to approximate mappings between infinite-dimensional spaces usingrelatively small datasets. The proposed DeepONet takes an arbitrary continuousrib geometry with control points as input and outputs continuous detailedinformation about the distribution of pressure and heat transfer around theprofiled ribs. The datasets needed to train and test the proposed DeepONetframework were obtained by simulating a 2D rib-roughened internal coolingchannel. To accomplish this, we continuously modified the input rib geometry byadjusting the control points according to a simple random distribution withconstraints, rather than following a predefined path or sampling method. Thestudied channel has a hydraulic diameter, Dh, of 66.7 mm, and alength-to-hydraulic diameter ratio, L/Dh, of 10. The ratio of rib center heightto hydraulic diameter (e/Dh), which was not changed during the rib profileupdate, was maintained at a constant value of 0.048. The ribs were placed inthe channel with a pitch-to-height ratio (P/e) of 10. In addition, we providethe 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 DeepONetparameters using the novel framework of stochastic gradient replica-exchangeMCMC.

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