网络模型
Cluster-based network model
摘要：
我们提出了一个自动化的数据驱动的方法，强大的非线性降阶建模的时间分辨快照数据。在运动学粗粒化中，快照被聚类成几个可代表整个系综的质心。动态被概念化为一个有向网络，其中的质心表示节点和有向边缘表示可能的有限时间转换。转换概率和时间是从快照数据中推断出来的。由此产生的集群为基础的网络模型构成了一个确定性随机灰箱模型解决相干结构的演变。该模型的动机是极限环动力学，说明了混沌洛伦兹吸引子，并成功地证明了层流二维混合层具有开尔文-亥姆霍兹涡和涡配对，并为一个驱动的湍流边界层与复杂的动态。基于聚类的网络建模开辟了一条有前途的新途径，与基于聚类或适当正交分解的其他模型降阶相比具有独特的优势。
英文摘要：
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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