  In this study, we propose a novel data-driven reduced-order model for complex
dynamics, including nonlinear, multi-attractor, multi-frequency, and multiscale
behaviours. The starting point is a fully automatable cluster-based network
model (CNM) (Li et al. J. Fluid Mech. vol.906, 2021, A21) which kinematically
coarse-grains the state with clusters and dynamically predicts the transitions
in a network model. In the proposed dynamics-augmented CNM (dCNM), the
prediction error is reduced with trajectory-based clustering using the same
number of centroids. The dCNM is first exemplified for the Lorenz system and
then implemented for the three-dimensional sphere wake featuring periodic,
quasi-periodic and chaotic flow regimes. For both plants, the dCNM
significantly outperforms the CNM in resolving the multi-frequency and
multiscale dynamics. This increased prediction accuracy is obtained by
stratification of the state space aligned with the direction of the
trajectories. Thus, the dCNM has numerous potential applications to a large
spectrum of shear flows, even for complex dynamics.
