Systematic Performance Assessment of Deep Material Networks for Multiscale Material Modeling
Xiaolong He, Haoyan Wei, Wei Hu, Henan Mao, C. T. Wu
TL;DR
This work systematically benchmarks structure-preserving DMN and its rotation-free IMN variant for multiscale material modeling. It analyzes how offline training choices and online solvers influence accuracy and efficiency, showing that DMN can generalize from linear training to nonlinear inelastic behavior while IMN achieves substantial offline speedups. The Newton-based online scheme further enhances IMN performance, yielding faster convergence with comparable accuracy to fixed-point methods. Overall, the study clarifies trade-offs between expressivity and computational cost, offering practical deployment guidance for offline training and online prediction in multiscale simulations.
Abstract
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.