Center for Biomedical Engineering, Brown University, Providence, Rhode Island 02912, USA.
Department of Mathematics, University College London, London WC1E 6BT, United Kingdom.
Chaos. 2019 Dec;29(12):123125. doi: 10.1063/1.5125493.
We use topological data analysis and machine learning to study a seminal model of collective motion in biology [M. R. D'Orsogna et al., Phys. Rev. Lett. 96, 104302 (2006)]. This model describes agents interacting nonlinearly via attractive-repulsive social forces and gives rise to collective behaviors such as flocking and milling. To classify the emergent collective motion in a large library of numerical simulations and to recover model parameters from the simulation data, we apply machine learning techniques to two different types of input. First, we input time series of order parameters traditionally used in studies of collective motion. Second, we input measures based on topology that summarize the time-varying persistent homology of simulation data over multiple scales. This topological approach does not require prior knowledge of the expected patterns. For both unsupervised and supervised machine learning methods, the topological approach outperforms the one that is based on traditional order parameters.
我们使用拓扑数据分析和机器学习来研究生物学中一个重要的集体运动模型[M. R. D'Orsogna 等人，物理评论快报 96,104302（2006）]。该模型描述了通过吸引力-排斥力等非线性相互作用的个体，并产生了集体运动，如聚集和碾磨。为了对大量数值模拟中的涌现的集体运动进行分类，并从模拟数据中恢复模型参数，我们将机器学习技术应用于两种不同类型的输入。首先，我们输入传统上用于集体运动研究的序参量的时间序列。其次，我们输入基于拓扑的度量，这些度量概括了模拟数据在多个尺度上的时变持久同调。这种拓扑方法不需要对预期模式有先验知识。对于无监督和有监督的机器学习方法，基于拓扑的方法都优于基于传统序参量的方法。
