Application of Low-Dimensional Manifold Modeling with Time Delay Embedding in Nonlinear Dynamics
Zihao Wang, Guiyong Zhang, Tiezhi Sun · International Journal of Computational Methods · 2025
The motion of a pitching airfoil at low Reynolds number and high angle of attack involves nonlinear dynamics and unstable characteristics, making it a fascinating area for research. In this study, the precise modeling of this complex fluid flow phenomenon is addressed. By combining manifold learning and time delay embedding theory, stable nonlinear low-dimensional manifolds are successfully extracted from the complex high-dimensional spatiotemporal data of the fluid system, simplifying the representation of intricate physical behaviors in space. Subsequently, utilizing the Least Absolute Shrinkage and Selection Operator (LASSO) model, we establish a set of ordinary differential equations governing the flow field, thereby automatically detecting and simplifying nonlinear terms to enhance understanding of the essence of the flow field. This research provides an efficient and accurate approach for the analysis and control of nonlinear dynamic systems.