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.

翻译：我们提出了一种基于高斯混合模型（GMMs）的新型无监督机器学习激波捕捉算法。所提出的GMM传感器在检测激波时展现出卓越的准确性，并且无需参数调整即可在多种测试案例中保持鲁棒性。我们将基于GMM的传感器与最新的替代方案进行了比较。所有方法均集成到高阶可压缩间断伽辽金求解器中，其中可通过调节人工黏度来捕捉激波。超声速测试案例（包括高雷诺数情况）展示了该传感器的性能，其表现与经过精细调优的最新传感器同样有效。节点型DG方法为子单元通量差分格式、超声速特征检测及网格加密等潜在应用提供了可能。该传感器具有自适应特性，且无需大量训练数据集即可运行，因此适用于复杂几何构型和多种流动配置。我们的研究揭示了以GMM传感器为代表的无监督机器学习方法在提升先进CFD代码稳健性与效率方面的潜力。