A Symbolic Regression Inspired Method for Compressible Flowfield Classification Through Local Characteristic Distribution

Abstract

The characteristic curve (characteristic) serves as a powerful tool for predicting the temporal evolution of solutions to conservation laws. This work proposes a framework for classifying compressible flowfields from the perspective of the local characteristic distribution of fluid governing equations. First, the symbolic regression (SR) method is employed to derive a 2D vortex indicator from data. Inspired by the SR result, the eigenvalue configurations of the gradient matrix of the characteristic eigenvalues along orthogonal directions in mathematics are found to exhibit a one-to-one correspondence with the localized flow structures in physics. Based on this discovery and analysis, this work pioneers a unified theoretical framework for compressible flowfield classification based on local characteristic distribution. The framework is generalized to 3D scenario and applicable to identifying critical flow structures including vortices, shock waves, expansion waves, and departure structures in complex flows. Extensive 2D and 3D numerical results validate the consistency between the practical performance and the theoretical analysis of the proposed framework. Classifying flowfields from the perspective of local characteristic distribution offers valuable insights in comprehending the generation, existence, and dissipation mechanisms of flow structures governed by fluid equations, such as shocks and vortices.

Keywords: Symbolic regression, conservation laws, evolution of characteristics, shock and vortex identification, flowfield classification