Juanmian Lei | Searcharxiv

arXiv2025

Interpretable data-driven turbulence modeling for separated flows using symbolic regression with unit constraints

Machine learning techniques have been applied to enhance turbulence modeling in recent years. However, the "black box" nature of most machine learning techniques poses significant interpretability challenges in improving turbulence models. This paper introduces a novel unit-constrained turbulence modeling framework using symbolic regression to overcome these challenges. The framework amends the constitutive equation of linear eddy viscosity models (LEVMs) by establishing explicit equations between the Reynolds stress deviation and mean flow quantities, thereby improving the LEVM model's predictive capability for large separated turbulence. Unit consistency constraints are applied to the symbolic expressions to ensure physical realizability. The effectiveness of the framework and the generalization capability of the learned model are demonstrated through its application to the separated flow over 2D periodic hills and a backward-facing step. Compared to the standard k-ε model, the learned model shows significantly improved predictive accuracy for anisotropic Reynolds stresses, velocity and skin friction, while exhibiting promising generalization capabilities across various scenarios.

physics.flu-dyn↗

arXiv2025

CTSR: Cartesian tensor-based sparse regression for data-driven discovery of high-dimensional invariant governing equations

Accurate and concise governing equations are crucial for understanding system dynamics. Recently, data-driven methods such as sparse regression have been employed to automatically uncover governing equations from data, representing a significant shift from traditional first-principles modeling. However, most existing methods focus on scalar equations, limiting their applicability to simple, low-dimensional scenarios, and failing to ensure rotation and reflection invariance without incurring significant computational cost or requiring additional prior knowledge. This paper proposes a Cartesian tensor-based sparse regression (CTSR) technique to accurately and efficiently uncover complex, high-dimensional governing equations while ensuring invariance. Evaluations on two two-dimensional (2D) and two three-dimensional (3D) test cases demonstrate that the proposed method achieves superior accuracy and efficiency compared to the conventional technique.

cs.LG↗