Cluster-based network model

POSTER

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 snap-shots 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.

Authors

  • Hao LI

    • Scicence and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha 410073,China

  • Daniel Fernex

    • Institut f\"ur Str\"omungsmechanik, Technische Universit\"at Braunschweig, Braunschweig, Germany

  • Richard Semaan

    • Institut f\"ur Str\"omungsmechanik, Technische Universit\"at Braunschweig, Braunschweig, Germany

  • Jianguo TAN

    • Scicence and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha 410073,China

  • Marek Morzy\’nski

    • Chair of Virtual Engineering, Pozna\'n University of Technology, Pozna\'n, Poland

  • Bernd R. Noack

    • Harbin Institute of Technology (Shenzhen), China
    • Harbin Institute of Technology (Shenzhen)
    • Center of Turbulence Control, Harbin Institute of Technology, Shenzhen 518058, China
    • HIT, China and TU Berlin, Germany