Mapping the Phase Diagram of the Vicsek Model with Machine Learning
2026-04-30 • Machine Learning
Machine Learning
AI summaryⓘ
The authors used machine learning to understand how groups of moving particles organize themselves in a model called the Vicsek flocking model. They ran many simulations with different settings and measured how particles moved over time. By grouping these measurements into phases like ordered, disordered, or mixed, they trained a neural network to predict these phases from the settings with high accuracy. This method helped them map out the different behaviors in the model more completely than just using the original simulations. Overall, their approach turns limited simulation data into a detailed picture of group motion behavior.
Vicsek flocking modelphase structuremachine learningK-Means clusteringneural network classifierphase diagramcollective motionorder-disorder transitionparameter spacedynamical observables
Authors
Grace T. Bai, Brandon B. Le
Abstract
In this study, we use machine learning to classify and interpolate the phase structure of the Vicsek flocking model across the three-dimensional parameter space $(η,ρ,v_0)$. We construct a dataset of simulated parameter points and characterize each point using long-time dynamical observables. These observables are then used as inputs to a K-Means clustering procedure, which assigns each point to a disorder, order, or coexistence phase. Using these clustered labels, we train a neural-network classifier to learn the mapping from model parameters to phase behavior, achieving a classification accuracy of 0.92. The resulting phase map resolves a narrow coexistence region separating the ordered and disordered phases and extends the inferred phase boundaries beyond the originally sampled simulation points. More broadly, this approach provides a systematic way to convert sparse simulation data into a global phase diagram for collective-motion models.