Fig. 5: Data-driven nonlinear SSM-reduced model on the unstable manifold of the steady solution of the flow past a cylinder.
From: Data-driven modeling and prediction of non-linearizable dynamics via spectral submanifolds
a Problem setup. b, c Snapshots of the steady solution and the time-periodic vortex-shedding solution (limit cycle, in magenta). d Trajectories projected on the 2-dim. subspace spanned by the two-leading POD modes of the limit cycle. e Model-based reconstruction of the test trajectory (not used in learning the SSM) in terms of velocities and pressures measured at a location q shown in plot a. f The SSM formed by the unstable manifold of the origin, along with some reduced trajectories, plotted over the unstable eigenspace UE ≡ E1; ∥UE⊥∥ denotes the normed projection onto the orthogonal complement UE⊥. g Same but projected over velocity and pressure coordinates.
