Conjugate Gradient Greedy Identification of Latent Dynamics from Parametric Flow Data.

In this talkl, we introduce an improved regression technique tailored for uncovering quadratic parametric reduced-order dynamical systems from empirical data. Our method, referred to as Conjugate Gradient Greedy Identification of Latent Dynamics (CG-GILD), builds upon the foundation laid by the GILD method introduced in the previous work [1]. We demonstrate a strategic organization of quadratic model coefficients that facilitates an elegant reformulation of the minimum-residual problem, leveraging the Frobenius norm. This reformulation yields a generalized Sylvester equation, efficiently solvable through an adapted conjugate gradient method. Through a meticulous comparative study, we illustrate that the enhanced version CG-GILD, exhibits superior convergence for quadratic model coefficients compared to the conventional GILD employing steepest gradient descent. Notably, this advancement translates into significantly fewer iterations, thereby reducing computational complexity substantially. To underscore the efficacy of our approach, we subject it to rigorous testing on the intricate task of analyzing Ahmed body flow with variable rear slant angle, showcasing its ability to tackle real-world dynamical system challenges.

[1] M. Oulghelou, A. Ammar, R. Ayoub,  Greedy Identification of Latent Dynamics from Parametric Flow Data (arxiv 2024).