Cluster-based network model
We propose an automatable data-driven methodology for robust nonlinear reduced-order modelling from time-resolved snapshot data. In the kinematical coarse-graining, the snapshots are clustered into few centroids representable for the whole ensemble. The dynamics is conceptualized as a directed network, where the centroids represent nodes and the directed edges denote possible finite-time transitions. The transition probabilities and times are inferred from the snapshot data. The resulting cluster-based network model constitutes a deterministic-stochastic grey-box model resolving the coherent-structure evolution. This model is motivated by limit-cycle dynamics, illustrated for the chaotic Lorenz attractor and successfully demonstrated for the laminar two-dimensional mixing layer featuring Kelvin-Helmholtz vortices and vortex pairing, and for an actuated turbulent boundary layer with complex dynamics. Cluster-based network modelling opens a promising new avenue with unique advantages over other model-order reductions based on clustering or proper orthogonal decomposition.