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.

翻译：本文设计了具备不确定性量化能力的代理模型，以有效提升带肋紊流内冷通道的热性能。为构建代理模型，我们采用深度算子网络（DeepONet）框架——一种新型神经网络，旨在利用相对较小的数据集逼近无限维空间之间的映射。所提出的DeepONet以任意包含控制点的连续肋条几何形状为输入，输出关于肋条周边压力与热传递分布的连续详细信息。训练和测试该DeepONet框架所需的数据集通过对二维带肋内冷通道的仿真获得。为此，我们根据带有约束的简单随机分布（而非遵循预设路径或采样方法）连续调整控制点以修改输入肋条几何形状。研究的通道水力直径Dh为66.7 mm，长径比L/Dh为10。肋条中心高度与水力直径之比e/Dh在肋条廓形更新过程中保持不变，恒定值为0.048。肋条以节距高度比P/e=10布置在通道中。此外，我们赋予所提代理模型有效的不确定性量化能力，这是通过将DeepONet框架转换为贝叶斯深度算子网络（B-DeepONet）实现的。B-DeepONet采用随机梯度副本交换MCMC的新框架从DeepONet参数的后验分布中进行采样。