Low-order nonlinear aerodynamics models from data with boundedness guarantees*

Obtaining predictive low-order models is a central challenge in fluid dynamics. Although data driven methods such as Sparse Identification of Nonlinear Dynamics (SINDy) have been widely used to model dynamical systems, these approaches can result in unbounded solutions when applied to complex flows. To address this, recent efforts have focused on promoting stability in data-driven models. In this work we leverage recent theoretical developments in characterizing the long-term boundedness and stability of dynamical systems. We propose a convex optimization approach to guarantee the long-term boundedness of a system, and incorporate the method into the SINDy framework to enable bounded model identification. Our approach is less conservative than prevailing methods, and benefits from being more computationally tractable. We demonstrate the effectiveness of our proposed method by successfully identifying a predictive low-order model of a stalled NACA-65(1)-412 airfoil with Re=20000, which has been a notoriously difficult problem for other data-driven modeling algorithms. We anticipate this work will benefit future efforts in modeling strongly nonlinear flows.