Identification of nonlinear dynamical system equations using dynamic mode decomposition under invariant quantity constraints

In this paper, an algorithm for identifying equations representing a continuous nonlinear dynamical system from a noise-free state and time-derivative state measurements is proposed. It is based on a variant of the extended dynamic mode decomposition. A particular attention is paid to guarantee that the physical invariant quantities stay constant along the integral curves. The numerical methodology is validated on a two-dimensional Lotka–Volterra system. For this case, the differential equations are perfectly retrieved from data measurements. Perspectives of extension to more complex systems are discussed.