Dynamic Mode Decomposition for Continuous Time Systems with the Liouville Operator

Dynamic mode decomposition (DMD) has become synonymous with the Koopman operator, where continuous time dynamics are discretized and examined using (i.e. composition) operators. Using newly introduced “occupation kernels,” present manuscript develops an approach to DMD that treats directly through Liouville operator. This outlines technical theoretical differences between Koopman-based for discrete systems Liouville-based systems, which includes examination of operators over several reproducing kernel Hilbert spaces. While modally unbounded, this introduces concept a scaled which, many dynamical is compact operator native space exponential dot product kernel. Compactness allows norm convergence DMD, decided advantage DMD.