Proper orthogonal decomposition (POD) is used to extract the spatially orthogonal coherent structures;

Dynamic mode decomposition (DMD) is used to capture the spatial-temporal coupling modes with a signal frequency and growth rate;

These approaches are applied to studying the physics of transonic buffet;

A criterion to select dominant DMD models is proposed to better retain the flow dynamics in transient regimes (from linear equilibrium state to the limit cycle);

Using higher-order DMD with criterion for reduced-order modeling of unsteady flows from a transient solution to the attractor;

Future works are developing efficient DMD-based approach to allow inputs (better than current approaches), improving the performance of DMD in modeling nonlinear flows, and developing machine-learning based mode decomposition techniques.