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.

翻译：深度材料网络（DMN）已成为多尺度材料建模的强大框架，能够高效且准确地预测不同尺度下的材料行为。与传统的纯数据驱动方法不同，DMN中的可训练参数具有明确的物理含义——它们编码了代表性体积单元（RVE）的几何特征，而非仅作为统计拟合参数。通过采用分层树状结构，DMN能够学习与微观结构几何相关的均质化行为。因此，它可仅在线弹性数据集上进行训练，同时在线预测时有效外推至非线性响应，这使其成为多尺度模拟中高效且可扩展的方法。从更广泛的视角来看，DMN可被视为一种物理信息驱动的降阶模型，能够捕捉控制宏观行为的关键微观力学特征。其层级化表述提供了紧凑且可解释的RVE响应表示，相比直接数值模拟显著降低了计算成本。本综述详细阐述了DMN的理论基础、训练方法及最新扩展，强调了其作为连接数据驱动学习与物理可解释多尺度建模的统一框架的作用。