Multi-Timescale System Separation via Data-Driven Identification Within a Singular Perturbation Framework

This paper presents a timescale separation method for realization-preserving reduced-order modeling of dynamic systems. While classical singular perturbation theory can be used to separate fast and slow states of multi-timescale systems in a standardized form, many real-world systems do not follow this form. Alternatively, geometric singular perturbation theory admits a more general nonstandard form, however it mainly focuses on analyzing the system dynamics in a transformed state space, which is not realization-preserving. Furthermore, existing methods typically assume that the locations and values of small parameters used to form the perturbed system are known, however for complex systems this may not be the case. The proposed approach integrates a data-driven method with singular perturbation theory to achieve timescale separation of multi-timescale systems without assuming prior knowledge of the small parameters. Furthermore, a sparsity-promoting data-driven approach allows the relative timescale of each state to be characterized, facilitating separation of systems with more than two timescales. Numerical examples illustrate the efficacy and computational efficiency of the proposed approach.