Deep Material Networks (DMNs) are structure-preserving, mechanistic machine learning models that embed micromechanical principles into their architectures, enabling strong extrapolation capabilities and significant potential to accelerate multiscale modeling of complex microstructures. A key advantage of these models is that they can be trained exclusively on linear elastic data and then generalized to nonlinear inelastic regimes during online prediction. Despite their growing adoption, systematic evaluations of their performance across the full offline-online pipeline remain limited. This work presents a comprehensive comparative assessment of DMNs with respect to prediction accuracy, computational efficiency, and training robustness. We investigate the effects of offline training choices, including initialization, batch size, training data size, and activation regularization on online generalization performance and uncertainty. The results demonstrate that both prediction error and variance decrease with increasing training data size, while initialization and batch size can significantly influence model performance. Moreover, activation regularization is shown to play a critical role in controlling network complexity and therefore generalization performance. Compared with the original DMN, the rotation-free Interaction-based Material Network (IMN) formulation achieves a 3.4x - 4.7x speed-up in offline training, while maintaining comparable online prediction accuracy and computational efficiency. These findings clarify key trade-offs between model expressivity and efficiency in structure-preserving material networks and provide practical guidance for their deployment in multiscale material modeling.

翻译：深度材料网络（DMNs）是一种结构保持型机理机器学习模型，其架构中嵌入了微观力学原理，因而具备强大的外推能力，在加速复杂微观结构的跨尺度建模方面展现出显著潜力。这类模型的关键优势在于：可仅在线性弹性数据上进行训练，而后在在线预测阶段泛化至非线性非弹性力学区域。尽管其应用日益广泛，但针对其在整个离线-在线流程中性能的系统性评估仍较为有限。本研究对DMNs的预测精度、计算效率和训练鲁棒性进行了全面的比较性评估。我们探究了离线训练选择（包括初始化方式、批处理大小、训练数据规模和激活正则化）对在线泛化性能及不确定性的影响。结果表明，预测误差和方差均随训练数据规模的增加而降低，而初始化方式和批处理大小可显著影响模型性能。此外，激活正则化被证明在控制网络复杂度从而影响泛化性能方面起着关键作用。与原始DMN相比，无旋转的基于相互作用的材料网络（IMN）公式在离线训练阶段实现了3.4倍至4.7倍的加速，同时保持了相当的在线预测精度和计算效率。这些发现阐明了结构保持型材料网络中模型表达能力与效率之间的关键权衡，并为其在跨尺度材料建模中的实际部署提供了实用指导。