Applied Koopman Theory for Partial Differential Equations and Data-Driven Modeling of Spatio-Temporal Systems

Figure 7

Reconstruction of the CQGLE dynamics of Figure 6(a) using a rank expansion. Shown are (a) a standard DMD approximation , (b) the CQGLE motivated , and (c) a quartic observable . The Koopman spectra for each observable are demonstrated in (d), (e), and (f) which accompany the observables of (a), (b), and (c), respectively. Note that the observable produces spectra which are most approximately purely imaginary which is expected of the periodic evolution. A visual inspection shows that the observable produces the best reconstruction.

(a)

(b)

(c)

(d)

(e)

(f)