关键词: 稀薄非平衡流, 极端随机树, 旋转不变性, 泛化性能, 数据驱动

Abstract: Adopting the numerical results from the Navier-Stokes equation and the UGKS method as the training data of the flow field samples, the Driven Nonlinear Constitutive Relations (DNCR) method constructs a high-dimensional complex nonlinear regression model for the heat flux/stress tensor and flow field characteristic parameters. The macro conservation equations are also solved by coupling data-driven nonlinear constitutive relations, and the numerical solution to the rarefied non-equilibrium flow to be predicted is obtained. However, not all features (such as velocity, pressure, and density) and outputs (such as heat flow and stress tensor) of the existing DNCR method are rotation invariants, and therefore the training model cannot be directly applied to rotated or translated coordinate systems. Aiming at this defect, this paper constructs a set of new features and outputs with the rotation invariant assumption, and optimizes all the training set features by combining the prediction results of the typical examples and the weight feedback. Meanwhile, parameter selection and optimization for the extreme random tree is conducted to improve the prediction range and generalization performance of the regression model, finally proposing an improved DNCR based on rotation invariants. The improvement in the new method is evaluated through two-dimensional hypersonic flow around the cylinder and lid driven flow under different flow conditions with different configurations compared with the original one. The results show that the use of rotation invariants can significantly improve the ability of the training model to adapt to coordinate system rotation and shape changes, enabling the DNCR with better generalization ability.

Key words: rarefied non-equilibrium flow, extremely randomized trees, rotation invariance, generalization ability, data-driven