论文标题
基于群集的网络模型
Cluster-based network model
论文作者
论文摘要
我们提出了一种可自动数据驱动的方法，用于从时间分辨快照数据中鲁棒的非线性还原模型。在运动学的粗粒剂中，快照聚集成整个合奏可代表的几个质心。动力学被概念化为有向网络，其中质心代表节点，而有向的边缘表示可能的有限时间过渡。从快照数据推断出过渡概率和时间。所得的基于群集的网络模型构成了确定性的灰色盒模型，可以解决相干结构的演变。该模型是由极限循环动力学的动力进行的，该模型为混沌洛伦兹吸引子说明，并成功证明了层次二维混合层，具有开尔文 - 霍尔姆·霍尔特兹（Kelvin-Helmholtz）涡流和涡旋配对，以及具有复杂动力学的驱动湍流边界层。基于群集的网络建模为基于聚类或正交分解的其他模型订单减少的独特优势开辟了一个有希望的新途径。
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.
