  We use topological data analysis and machine learning to study a seminal
model of collective motion in biology [D'Orsogna et al., Phys. Rev. Lett. 96
(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 in 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.
