Physics-informed unsupervised machine learning for 4D-STEM materials characterization

Four-dimensional scanning transmission electron microscopy (4D-STEM) provides bimodal real- and reciprocal-space information and forms the basis of various STEM imaging techniques, including standard bright-field and annular dark-field imaging, ptychography, and differential phase contrast. Advancements in detection systems have rendered 4D-STEM increasingly practical, while also enabling the acquisition of large datasets. Here, we propose a comprehensive workflow that integrates 4D-STEM with unsupervised machine learning while incorporating electron microscopy knowledge. The workflow comprises three key substeps: data preprocessing, dimensionality reduction, and clustering. We detail how physical insight from electron microscopy is embedded into each substep. In the data preprocessing substep, feature extraction is performed such as noncentrosymmetry based on diffraction physics. In the dimensionality reduction substep, we develop a constrained nonnegative matrix factorization that incorporates physics-based constraints for diffraction and corresponding real-space map. In the clustering substep, diffraction similarity is defined in place of conventional cosine similarity, fully exploiting the bimodal nature of 4D-STEM data. The effectiveness of the proposed workflow is demonstrated using both simulated datasets and experimental data from two representative specimens: twist domains of monolayer MoS ₂ and small crystalline precipitates in a metallic glass ZrCuAl. These results demonstrate that the proposed workflow enables advanced characterization of unknown materials that are difficult to achieve using conventional methods, highlighting the potential of physics-informed unsupervised machine learning combined with 4D-STEM.