深度材料网络在多尺度材料建模中实现高效精准预测,提升训练速度与泛化能力。
Systematic Performance Assessment of Deep Material Networks for Multiscale Material Modeling
- 结构保持的机器学习架构融合微力学原理,支持从线性到非线性场景的外推预测。
- 训练数据量增加可降低预测误差与方差,初始化和批量大小显著影响模型性能。
- 新提出的无旋转交互式材料网络使离线训练提速3.4至4.7倍,适合工程部署。
深度材料网络(DMNs)是结构保持的机制性机器学习模型,将微力学原理嵌入架构中,具备强大的外推能力,有望加速复杂微结构的多尺度建模。其关键优势在于仅需在线弹性数据训练,即可在在线预测中推广至非线性非弹性范围。尽管应用日益广泛,其在完整离线-在线流程中的系统性评估仍有限。本文对DMNs进行了全面比较评估,涵盖预测精度、计算效率与训练鲁棒性。研究考察了离线训练选择的影响,包括初始化、批量大小、训练数据规模及激活正则化对在线泛化性能与不确定性的作用。结果表明,随着训练数据量增加,预测误差与方差均下降;初始化与批量大小显著影响模型表现。此外,激活正则化在控制网络复杂度与泛化性能方面起关键作用。相较于原始DMN,无旋转的基于交互的材料网络(IMN)在离线训练中实现3.4至4.7倍加速,同时保持相当的在线预测精度与计算效率。这些发现明确了结构保持材料网络中表达能力与效率之间的权衡,并为多尺度材料建模中的实际部署提供指导。
原文摘要 · Abstract (English)
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.
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