Autoencoder-Based Unsupervised Identification of Nonequilibrium Phases in Sheared Binary Colloids

Abstract

Identifying nonequilibrium phases in particle systems remains a major challenge because they often exhibit complex and spatially heterogeneous structures without long-range order. Here, we develop an unsupervised machine-learning framework for classifying such nonequilibrium phases by integrating Fourier-based preprocessing, an autoencoder, and a Gaussian mixture model (GMM). Specifically, we transform global spatial configurations into Fourier space and use the amplitudes of Fourier coefficients as inputs to the autoencoder. This preprocessing suppresses spatial noise while preserving phase-specific structural features and physical interpretability. We demonstrate the effectiveness of this framework using a binary charged colloidal system under steady shear flow, where the competition between Coulomb interactions and shear gives rise to three nonequilibrium phases characterized by distinct local structures. The encoded latent space reveals well-separated clusters that are robustly identified by the GMM, enabling the construction of a nonequilibrium phase diagram based on cluster membership probabilities. The resulting phase boundaries are consistent with those independently obtained from radial distribution function analysis and unsupervised anomaly detection. These results demonstrate that autoencoder-based unsupervised learning provides an effective framework for identifying nonequilibrium phases in complex particle systems.