Novel material representation method via a deep learning model for multi-scale topology optimization

In this paper, a novel deep learning-aided material representation scheme for multi-scale topology opti-mization is proposed. This method shows that it is possible to determine a general-purpose mapping from a low-dimensional variable to the image of microstructures. A deep generative model learns features from microstructural images to find manifolds defined in the low-dimensional latent space, then a regression model is trained to fit the equivalent material properties. After training, the generator and predictor networks are integrated into the multi-scale topology optimization process to reduce the number of design variables and replace the homogenization computation, respectively. With the proposed material representation method, the optimization algorithm converges faster, while automatically satisfying complicated geometrical restrictions without any additional constraints. Due to the generator network, the microstructures can be interpolated over the latent manifold. It enables the multi-scale topology optimization can be conducted over an irregular design domain with unstructured mesh. The effectiveness of this method is tested with two simple manually designed microstructures and a complex one obtained by inverse homogenization, and its performance is discussed based on the number of design variables, computational efficiency, and optimized multi-scale design results. The optimization performance tends to be improved as the latent dimensions increase. The results show that, on average, the elapsed time per iteration of the proposed method is close to two percent of that of conventional methods. By means of the ability to interpolate microstructures, a high-resolution full-scale realization can be obtained from a lower-resolution design, and the proposed method can utilize an unstructured mesh in multi-scale topology optimization.