Linearized analyses of fluid flows from nonlinear simulation data*

The Dynamic Mode Decomposition (DMD) has been consolidated as a basic tool for data-driven analysis of fluid flows, allowing simultaneous identification of coherent structures and their dynamics from time-resolved measurements. However, with a linear regression at its core, DMD is unable to produce accurate models from recordings of dynamics that are inherently nonlinear, such as the response to large perturbations and the evolution on chaotic attractors. Fortunately, the Linear and Nonlinear Disambiguation Optimization (LANDO) enables DMD-like, data-driven analysis of high-dimensional dynamical systems that is robust to strong nonlinearities. Leveraging kernel regression, LANDO produces an accurate model for the evolution of the system, isolates the purely nonlinear contributions to the dynamics in the data, and identifies interpretable coherent structures associated with the linear part of the dynamics. We explore the potential of LANDO to perform linearized analyses of fluid flows, such as stability, Floquet, transient growth, and resolvent analysis, from snapshots of nonlinear simulations.