Cluster-based network model

Abstract

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.

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• Stabilization of the fluidic pinball with gradient-enriched machine learning control
• Cluster-based hierarchical network model of the fluidic pinball -- Cartographing transient and post-transient, multi-frequency, multi-attractor behaviour
• Stabilization of a multi-frequency open cavity flow with gradient-enriched machine learning control
• Trajectory-optimized cluster-based network model for the sphere wake
• Machine-learning identification of the variability of mean velocity and turbulence intensity for wakes generated by onshore wind turbines: Cluster analysis of wind LiDAR measurements
• Load estimation in unsteady flows from sparse pressure measurements: Application of transition networks to experimental data
• Discrete vortex-based broadcast mode analysis for mitigation of dynamic stall