标题： 融合-深度算子网络：一种用于几何相关高超音速和超音速流的数据高效神经算子 显示英文标题

标题： Fusion-DeepONet: A Data-Efficient Neural Operator for Geometry-Dependent Hypersonic and Supersonic Flows

摘要： 形状优化在航天器设计中至关重要，包括再入系统和推进系统部件，因为它直接影响气动效率、结构完整性和整体任务成功。快速而准确地预测外部和内部流动可以加速设计迭代。为此，我们开发了DeepONet的新变体，称为Fusion-DeepONet，作为几何依赖的高超音速和超音速流动场的快速代理模型。我们在学习两个外部高超音速流动和一个超音速形状依赖的内部流动问题中评估了Fusion-DeepONet。首先，我们将Fusion-DeepONet的性能与最先进的神经算子进行比较，以学习两种网格类型（均匀笛卡尔网格和不规则网格）下半椭圆钝体周围的无粘高超音速流动。在均匀网格上，Fusion-DeepONet的准确性与参数条件U-Net相当，而在不规则网格上优于MeshGraphNet和Vanilla-DeepONet。Fusion-DeepONet所需的可训练参数显著少于U-Net、MeshGraphNet和FNO。对于第二个高超音速问题，我们设置Fusion-DeepONet从几何形状和自由流马赫数映射到以高超音速飞行的再入舱周围的温度场。然后，这个快速代理模型被改进以预测温度的空间导数，从而准确预测再入舱表面的热流。为了提高空间导数预测的准确性，我们引入了一个计算开销最小的导数增强损失项。对于第三个问题，我们展示了Fusion-DeepONet在学习收敛-扩散喷管配置中的几何依赖超音速流动方面优于MeshGraphNet。对于所有问题，我们使用高保真模拟，采用高阶熵稳定DGSEM求解器生成具有有限样本的训练数据集。 显示英文摘要

摘要： Shape optimization is essential in aerospace vehicle design, including reentry systems, and propulsion system components, as it directly influences aerodynamic efficiency, structural integrity, and overall mission success. Rapid and accurate prediction of external and internal flows accelerates design iterations. To this end, we develop a new variant of DeepONet, called Fusion-DeepONet as a fast surrogate model for geometry-dependent hypersonic and supersonic flow fields. We evaluated Fusion-DeepONet in learning two external hypersonic flows and a supersonic shape-dependent internal flow problem. First, we compare the performance of Fusion-DeepONet with state-of-the-art neural operators to learn inviscid hypersonic flow around semi-elliptic blunt bodies for two grid types: uniform Cartesian and irregular grids. Fusion-DeepONet provides comparable accuracy to parameter-conditioned U-Net on uniform grids while outperforming MeshGraphNet and Vanilla-DeepONet on irregular grids. Fusion-DeepONet requires significantly fewer trainable parameters than U-Net, MeshGraphNet, and FNO. For the second hypersonic problem, we set up Fusion-DeepONet to map from geometry and free stream Mach number to the temperature field around a reentry capsule traveling at hypersonic speed. This fast surrogate is then improved to predict the spatial derivative of the temperature, resulting in an accurate prediction of heat flux at the surfaces of the capsule. To enhance the accuracy of spatial derivative prediction, we introduce a derivative-enhanced loss term with the least computation overhead. For the third problem, we show that Fusion-DeepONet outperforms MeshGraphNet in learning geometry-dependent supersonic flow in a converging-diverging nozzle configuration. For all the problems, we used high-fidelity simulations with a high-order entropy-stable DGSEM solver to generate training datasets with limited samples.