Machine learning techniques for understanding pattern formation and self-assembly in active colloidal systems

Active colloidal matter provides a rich setting for the emergence of nonequilibrium patterns, dynamic aggregates, and self-assembled structures. Understanding how such organization arises from microscopic interactions, fluctuations, and sustained external driving remains a central challenge in soft-matter physics. This is largely because traditional theoretical and computational approaches often struggle with nonlinear dynamics, multiscale behavior, and high-dimensional parameter spaces. In this context, machine learning (ML) is increasingly used to identify relevant order parameters, classify dynamical regimes, predict emergent structures, infer assembly pathways, and guide the design and control of target states. This review examines how ML methods are incorporated into the study of pattern formation and self-assembly across both equilibrium and active colloidal systems. The discussion is organized around the analysis and representation of data pertaining to complex nonequilibrium systems, the prediction of dynamical and structural outcomes, the inference of latent variables and assembly pathways, and the design or control of target states through generative models and reinforcement learning strategies. We also discuss hybrid approaches that incorporate physical constraints to improve interpretability, robustness, and generalization. By focusing on the interplay between machine learning and nonequilibrium soft-matter physics, we highlight both the opportunities and the open challenges of the field, including the connection between learned representations and physical variables, limited extrapolation capability across state space, and the need for reproducible benchmarks and high-quality datasets. Overall, we argue that ML is emerging as an important complement to theory and simulation in the study of active colloidal self-assembly, not as a replacement for physical modeling, but as a means to accelerate discovery and deepen understanding of emergent nonequilibrium organization.