Data-driven approach for dynamic homogenization using meta learning

Abstract

Studying wave propagation in heterogeneous structures can become computationally expensive because they rely on detailed finite element models to ensure accuracy. This problem is exacerbated if short wavelengths need to be captured, which leads to the need for a very fine discretization of the temporal domain. In this work, we propose a method for predicting the dynamic response of large arbitrary heterogeneous structures that leverages state-of-the-art machine learning techniques to develop a surrogate model for a unit cell and effectively homogenize it. Such a surrogate model represents the global behavior of the unit cell while preserving the local information and/or the effect of heterogeneities on the global behavior. To generate our model, we propose a training scheme inspired from meta-learning that expands the operational frequency spectrum and improves the prediction resolution of the unit cell.The proposed approach is not limited to only a particular type of material of heterogeneity in the unit cell, as demonstrated through linear as well as hyperelastic unit cells with and without holes. We also illustrate how to implement a surrogate unit cell in large arbitrary structures to study wave propagation phenomena. We present our method’s ability by comparing its results with those obtained via high-fidelity finite element simulations. Our findings indicate that using surrogate unit cells can dramatically boost the computational efficiency and simplicity to analyze large structures, thus enabling their applications in areas such as band structure optimization and acoustic wave management, to name a few.