Modeling Partially Unknown Dynamics with Continuous Time DMD*

This manuscript addresses the problem of the data driven modeling of a dynamical system in the presence of partially known dynamics using an operator theoretic dynamic mode decomposition (DMD) approach. The method relies on the linearity of the Liouville operator with respect to the dynamics together with established relations between Liouville operators and occupation kernels, which embed trajectory data as a function within a reproducing kernel Hilbert space. The linearity allows for the known portion of the dynamics to be subtracted from the overall dynamics, and the Liouville operator corresponding to the unknown dynamics may thus be isolated. A model for the unknown portion of the dynamical systems may then be obtained from observed trajectory data, and this model may then be utilized for predicting future states.