Multi-objective Bayesian optimization (MOBO) is an efficient and robust optimization framework for expensive functions. In this work, we use MOBO to optimize the free parameters of a high-order nonlinear weighted essentially non-oscillatory (WENO) reconstruction scheme to devise a model for implicit large eddy simulations. We concurrently optimize for a low dispersion error and sufficient shock-capturing ability for compressible flows as well as for physically consistent transition occurring in under-resolved flow regions. With our approach, we follow the genealogy of designing implicit sub-grid models. Yet, in contrast to previous works that were limited to incompressible flows, our model is also applicable to compressible flows. Validated results show that the model is able to decrease excessive dissipation in continuous flow regimes, to capture shocks with little dispersive and dissipative errors while achieving a well shaped vortical structures. The proposed framework is general and can be used to design a physically consistent numerical scheme for under-resolved compressible-flow simulations.

多目标贝叶斯优化 (MOBO) 是一种针对昂贵函数的高效且稳健的优化框架。在这项工作中，我们使用 MOBO 来优化高阶非线性加权基本非振荡 (WENO) 重建方案的自由参数，以设计用于隐式大涡模拟的模型。我们同时优化了可压缩流动的低分散误差和足够的冲击捕获能力，以及在解析不足的流动区域中发生的物理一致过渡。通过我们的方法，我们遵循设计隐式子网格模型的谱系。然而，与以前仅限于不可压缩流动的工作相比，我们的模型也适用于可压缩流动。验证结果表明，该模型能够减少连续流动状态下的过度耗散，捕获具有很少分散和耗散误差的冲击，同时实现形状良好的涡旋结构。所提出的框架是通用的，可用于为欠解析可压缩流模拟设计物理一致的数值方案。