Analyzing Collective Motion with Machine Learning and Topology

TL;DR

This paper combines topological data analysis and machine learning to classify and analyze collective motion in biological models, outperforming traditional methods and enabling parameter recovery without prior pattern knowledge.

Contribution

It introduces a topological approach to classify collective behaviors and recover model parameters, outperforming traditional order parameter-based methods.

Findings

Topological measures outperform traditional order parameters in classification accuracy.

Machine learning effectively recovers model parameters from simulation data.

Topological approach does not require prior knowledge of emergent patterns.

Abstract

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.