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. (C) 2019 Academie des sciences. Published by Elsevier Masson SAS.