Data-driven reduced-order modeling for nonautonomous dynamical systems in multiscale media

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In this article, we present data-driven reduced-order modeling for nonautonomous dynamical systems in multiscale media using Koopman operators.

• Different from the case of autonomous dynamical systems, the Koopman operator family of nonautonomous dynamical systems significantly depend on a time pair.
• In order to effectively estimate the time-dependent Koopman operators, a moving time window is used to decompose the snapshot data, and the extended dynamic mode decomposition method is applied to computing the Koopman operators in each local temporal domain.
• Many physical properties in multiscale media often vary in very different scales.