Deep neural networks for parameterized homogenization in concurrent multiscale structural optimization

Concurrent multiscale structural optimization is concerned with the improvement of macroscale structural performance through the design of microscale architectures. The multiscale design space must consider variables at both scales, so design restrictions are often necessary for feasible optimization. This work targets such design restrictions, aiming to increase microstructure complexity through deep learning models. The deep neural network (DNN) is implemented as a model for both microscale structural properties and material shape derivatives (shape sensitivity). The DNN’s profound advantage is its capacity to distill complex, multidimensional functions into explicit, efficient, and differentiable models. When compared to traditional methods for parameterized optimization, the DNN achieves sufficient accuracy and stability in a structural optimization framework. Through comparison with interface-aware finite element methods, it is shown that sufficiently accurate DNNs converge to produce a stable approximation of shape sensitivity through back propagation. A variety of optimization problems are considered to directly compare the DNN-based microscale design with that of the Interface-enriched Generalized Finite Element Method (IGFEM). Using these developments, DNNs are trained to learn numerical homogenization of microstructures in two and three dimensions with up to 30 geometric parameters. The accelerated performance of the DNN affords an increased design complexity that is used to design bio-inspired microarchitectures in 3D structural optimization. With numerous benchmark design examples, the presented framework is shown to be an effective surrogate for numerical homogenization in structural optimization, addressing the gap between pure material design and structural optimization.