We present a novel unsupervised machine learning shock capturing algorithm
based on Gaussian Mixture Models (GMMs). The proposed GMM sensor demonstrates
remarkable accuracy in detecting shocks and is robust across diverse test cases
without the need for parameter tuning. We compare the GMM-based sensor with
state-of-the-art alternatives. All methods are integrated into a high-order
compressible discontinuous Galerkin solver where artificial viscosity can be
modulated to capture shocks. Supersonic test cases, including high Reynolds
numbers, showcase the sensor's performance, demonstrating the same
effectiveness as fine-tuned state-of-the-art sensors. %The nodal DG aproach
allows for potential applications in sub-cell flux-differencing formulations,
supersonic feature detection, and mesh refinement. The adaptive nature and
ability to function without extensive training datasets make this GMM-based
sensor suitable for complex geometries and varied flow configurations. Our
study reveals the potential of unsupervised machine learning methods,
exemplified by the GMM sensor, to improve the robustness and efficiency of
advanced CFD codes.

我们提出了一种基于高斯混合模型（GMMs）的新颖无监督机器学习激波捕获算法，在不需要参数调整的情况下，该算法能够准确检测激波并在不同测试案例中展现出强大的鲁棒性。通过与最先进的替代方法进行比较，并将所有方法集成到一个高阶可压间断 Galerkin 求解器中，其中的人工粘性可以调节以捕获激波，我们展示了基于 GMM 的传感器在超音速测试案例中的性能，包括高雷诺数，其效果与精心调整的最先进传感器相当。这种基于 GMM 的传感器具有自适应特性，能够在复杂几何和多样化流体配置中发挥作用，无需大量的训练数据集，适合于复杂的计算流体力学代码，揭示了无监督机器学习方法（如 GMM 传感器）提高先进 CFD 代码的鲁棒性和效率的潜力。