Existing numerical schemes used to solve the governing equations for compressible flow suffer from dissipation errors which tend to smear out sharp discontinuities. Hybrid schemes show potential improvements in this challenging problem; however, the solution quality of a hybrid scheme heavily depends on the criterion to switch between the different candidate reconstruction functions. This work presents a new type of switching criterion (or selector) using machine learning techniques. The selector is trained with randomly generated samples of continuous and discontinuous data profiles, using the exact solution of the governing equation as a reference. Neural networks and random forests were used as the machine learning frameworks to train the selector, and it was later implemented as the indicator function in a hybrid scheme which includes THINC and WENO-Z as the candidate reconstruction functions. The trained selector has been verified to be effective as a reliable switching criterion in the hybrid scheme, which significantly improves the solution quality for both advection and Euler equations.

用于求解可压缩流控制方程的现有数值方案存在耗散误差，这些误差往往会掩盖尖锐的不连续性。混合方案显示了在这一具有挑战性的问题上的潜在改进；但是，混合方案的解决方案质量在很大程度上取决于在不同候选重建函数之间切换的标准。这项工作提出了一种使用机器学习技术的新型切换标准（或选择器）。使用控制方程的精确解作为参考，用连续和不连续数据配置文件的随机生成样本训练选择器。神经网络和随机森林被用作机器学习框架来训练选择器，后来又以THINC和WENO-Z作为候选重建函数的混合方案实现为指标函数。经过训练的选择器已被证明可有效用作混合方案中的可靠切换准则，从而显着提高平流方程和Euler方程的解质量。