A data-driven two-branch deep neural network (DNN), to be referred to as \(\lambda \)-DNN, used to predict scalar fields is presented. The network architecture consists of two separate branches (input layers) connected to the main one towards its output. In multi-disciplinary shape optimization problems, such as those this paper is dealing with, the input to the \(\lambda \)-DNN contains data relevant to the geometrical shape and the case itself. Herein, the \(\lambda \)-DNN is used in conjugate heat transfer (CHT) analysis and shape optimization problems, synergistically with codes simulating flows over the fluid domain and solving the heat conduction equations over the solid one. It is used to optimize a duct and an internally cooled turbine blade-airfoil surrounded by hot gas. The \(\lambda \)-DNNs, after being trained on fields computed using the CHT solver, are used as surrogates for either the heat conduction equation solver of the solid domain, replicating either one out of the two disciplines of the problem or the coupled CHT solver.

提出了一种数据驱动的两分支深度神经网络（DNN），称为\（\ lambda \）- DNN，用于预测标量场。网络体系结构由两个独立的分支（输入层）组成，这些分支与主分支相连，并朝主分支输出。在多学科形状优化问题中（例如本文要解决的问题），\（\ lambda \）- DNN的输入包含与几何形状和壳体本身相关的数据。在这里，\（\ lambda \）-DNN用于共轭传热（CHT）分析和形状优化问题，并与模拟流体域内的流动并求解固体介质上的热传导方程的代码协同作用。它用于优化管道和被热气体包围的内部冷却的涡轮叶片翼型。的\（\拉姆达\） -DNNs，对字段被训练使用所述CHT解算器来计算后，被用作替代物或者热传导方程的固体结构域，复制任何一个出来的问题或两个学科的解算器耦合CHT求解器。