Machine learning based asymptotic homogenization and localization: Predictions of key local behaviors of multiscale configurations bearing microstructural varieties
Zhengcheng Zhou, Yichao Zhu, Xu Guo
Abstract
Abstract In this article, a general framework is devised for reliable predictions over the local behaviors, such as the failure strength and stress intensity factor, of multiscale configurations bearing microstructural varieties. Methodologically, a mutually complementing use of asymptotic analysis and machine learning is addressed. On using asymptotic analysis, we manage to identify several key but implicit interrelationships, which link the local quantities of our interest with other onsite mean‐field quantities. Then these identified interrelationships are represented by neural networks in an offline stage, where the training data are also generated based on the formulation devised through asymptotic analysis. Then for the upcoming online simulation, those desired local behaviors can be quickly captured without resolving the microstructural configurations. Numerical examples are presented showing that for relatively complex multiscale configurations, the predicting error here can be theoretically controlled at a satisfactory level.