Journal
CHAOS
Volume 29, Issue 12, Pages -Publisher
AMER INST PHYSICS
DOI: 10.1063/1.5125493
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Funding
- National Science Foundation (NSF) [DMS 1641020]
- NSF [1854703, DMS-1638521, DMS-1813752]
- National Cancer Institute IMAT Program [R21CA212932]
- American Mathematical Society's Mathematical Research Community
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1854703] Funding Source: National Science Foundation
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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. (C) 2019 Author(s).
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