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

Figure 1

The left panel illustrates the nonlinear manifold on which the dynamical system defined by in (2) generates a solution. DMD approximates the evolution on this manifold by a least-square fit linear dynamical system. In contrast, the selection of appropriate observables define a Koopman operator that helps linearize the manifold so that a least-square fit linear dynamical system provides a much better approximation to the system (right panel).