Transformer-driven classification of soft condensed matter via reference-based data embedding

Colloidal suspensions exhibit diverse phases from fluid-like to solid-like, which are critical for numerous industrial applications. However, accurately identifying their phases remains a challenge, as they depend on a complex interplay of solid volume fraction, particle size distribution, and interparticle interactions. Near phase boundaries, subtle microstructural changes can induce drastic macroscopic property variations, yet these differences are often indistinguishable through conventional observation. To overcome these limitations and the high computational costs of long-time simulations, we propose a transformer-driven framework based on reference-based data embedding. Unlike standard point cloud models that directly embed positions, our approach utilizes particle stress information as the primary feature while using spatial coordinates solely as a reference to map interparticle relationships. This allows the transformer-driven model to effectively capture structural characteristics at both local and global scales. By training the model exclusively on unambiguous regions far from phase boundaries to prevent mislabeling, we successfully predicted the complete phase diagram, which was further validated through theoretical and statistical analysis. Notably, our methodology significantly alleviates the need to monitor long-term structural convergence, which is typically challenging due to the inherently slow phase evolution in attractive colloidal systems. This framework provides a robust and cost-effective tool for the systematic discovery and reverse engineering of complex soft condensed matter.