Mapping the Phase Diagram of the Vicsek Model with Machine Learning

Forum topic · 小凯 · 2026-05-02

Summary

Researchers Jonathan Bongolan, Guillermo Romer, and Christian Alis apply machine learning to classify and interpolate the phase structure of the Vicsek flocking model across its three-dimensional parameter space (eta, rho, v_0). They build a dataset of simulated parameter points, characterizing each point with long-time dynamical observables. These observables serve as inputs to a K-Means clustering procedure that assigns each point to a disorder, order, or coexistence phase. The clustered labels are then used to train a neural-network classifier mapping model parameters to phase behavior, achieving a classification accuracy of 0.92. The resulting phase diagram resolves the narrow coexistence region separating ordered and disordered phases and extends inferred phase boundaries beyond the originally sampled simulation points. The work, published as arXiv:2604.28167, offers a systematic pipeline for turning sparse simulation data into global phase diagrams of collective motion models, bridging unsupervised clustering and supervised classification in computational physics.

Paper Overview

Field: ML/Physics
Authors: Jonathan Bongolan, Guillermo Romer, Christian Alis
Published: 2026-04-30
arXiv: 2604.28167

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 (eta, rho, 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 diagram resolves the 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 pipeline for transforming sparse simulation data into global phase diagrams of collective motion models.

Key Takeaways

ML-driven phase classification: K-Means clustering on long-time dynamical observables labels simulated parameter points as disorder, order, or coexistence phases without hand-crafted phase criteria.
Neural-network interpolation: A classifier trained on clustered labels achieves 0.92 accuracy, enabling interpolation of the phase diagram across the (eta, rho, v_0) parameter space.
Resolving the coexistence region: The reconstructed phase diagram captures the narrow coexistence band between ordered and disordered phases and extrapolates boundaries beyond sampled points.
Generalizable methodology: The workflow offers a template for building global phase diagrams from sparse simulation data in active matter and collective motion research.