Active matter is a relatively new subfield of nonequilibrium physics, where characterizing phase transitions and discovering new phases are key to understanding the collective behavior of systems in the thermodynamic limit. While studies have investigated phase transitions at equilibrium, a central question in nonequilibrium physics — and active matter in particular — is whether there exist novel types of phase transitions that are absent or yet to be discovered in equilibrium systems. This question was highlighted by the pioneering work of Vicsek and his colleagues, who discovered a qualitatively new phase transition that was naively believed to be forbidden by the Mermin–Wagner theorem. This discovery sparked the emergence of the field of active matter. More recently, phenomena such as phase separation and cluster formation in active matter have become intriguing topics of study.

Machine learning has attracted considerable attention due to its unprecedented success in image recognition/generation, natural language processing, and other domains; it has been applied in many areas across physics. Particularly, machine learning techniques are used for physical simulations and the identification of phase transitions. However, to date, the application of clustering algorithms to active matter remains relatively underexplored — despite clustering being a central topic in machine learning and its application to active matter being conceptually straightforward.

This study explores the possibility of applying clustering algorithms to active matter. Specifically, we begin with the Vicsek model, chosen for its simplicity and historical significance as one of the earliest models in active matter research. Given the wide variety of clustering algorithms available, the first challenge lies in selecting an appropriate one. In this work, we focus on Density-Based Spatial Clustering of Applications with Noise (DBSCAN), a widely used clustering method in engineering, because its control parameters can be meaningfully interpreted within the context of the Vicsek model. We first analyze the mathematical relationship between DBSCAN and the Vicsek model. Then, we apply DBSCAN to simulation data of the Vicsek model to identify the emergence of possible new phases. We introduce a novel order parameter based on DBSCAN to characterize any such newly discovered phases. Finally, we examine the robustness of the DBSCAN-defined cluster phase in the thermodynamic limit by comparing the results with those obtained using the mean-shift algorithm, which shares the same control parameter as DBSCAN.

These findings may offer a new perspective on active matter and how machine learning algorithms can be utilized for physics.

(Written by Hideyuki Miyahara on behalf of all authors.)

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