The Deep Material Network (DMN) has emerged as a powerful framework for multiscale materials modeling, enabling efficient and accurate prediction of material behavior across different length scales. Unlike conventional data-driven approaches, the trainable parameters in DMN possess clear physical interpretations-they encode the geometric characteristics of representative volume elements (RVEs) rather than serving as purely statistical fitting parameters . By employing a hierarchical tree structure, DMN learns the homogenization behavior associated with microstructural geometry. Consequently, it can be trained exclusively on linear elastic datasets while effectively extrapolating to nonlinear responses during online prediction, making it a highly efficient and scalable approach for multiscale simulations. From a broader perspective, DMN can be viewed as a physics-informed reduced-order model that captures the essential micromechanical features governing macroscopic behavior. Its hierarchical formulation provides a compact yet interpretable representation of the RVE response, significantly reducing computational costs compared to direct numerical simulations. This review elaborates on the theoretical foundation, training methodology, and recent extensions of DMN, emphasizing its role as a unifying framework that connects data-driven learning with physically interpretable multiscale modeling.

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