Mapping the Phase Diagram of the Vicsek Model with Machine Learning
TLDR
Machine learning is used to map the 3D phase diagram of the Vicsek flocking model, revealing a narrow coexistence region.
Key contributions
- Applied K-Means clustering to classify Vicsek model phases using long-time dynamical observables.
- Trained a neural network classifier to map model parameters to phase behavior with 0.92 accuracy.
- Resolved a narrow coexistence region and extended phase boundaries in the 3D parameter space.
- Developed a systematic ML approach to generate global phase diagrams from sparse simulation data.
Why it matters
This paper offers a systematic machine learning approach to map complex phase diagrams from limited simulation data. It provides a more complete understanding of the Vicsek model's phase structure, including previously unresolved regions. This method is broadly applicable to other collective-motion models.
Original 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.
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