An indirect design representation for topology optimization using variational autoencoder and style transfer

In this paper we propose an indirect low-dimension design representation to enhance topology optimization capabilities. Established topology optimization methods, such as the Solid Isotropic Material with Penalization (SIMP) method, can solve large-scale topology optimization problems efficiently, but only for certain problem formulation types (e.g., those that are amenable to efficient sensitivity calculations). The aim of the study presented in this paper is to overcome some of these challenges by taking a complementary approach: achieving efficient solution via targeted design representation dimension reduction, enabling the tractable solution of a wider range of problems (e.g., those where sensitivities are expensive or unavailable). A new data-driven design representation is proposed that uses an augmented Variational Autoencoder (VAE) to encode 2D topologies into a lower-dimensional latent space, and to decode samples from this space back into 2D topologies. Optimization is then performed in the latent space as opposed to the image space. Established topology optimization methods are used here as a tool to generate a data set for training by changing problem conditions systematically. The data is generated using problem formulations that are solvable by SIMP, and are related to (but distinct from) the desired design problem. We further introduce augmentations to the VAE formulation to reduce unrealistic scattering of small material clusters during topology generation, while ensuring diversity of the generated topologies. We compare computational expense for solving a heat conduction design problem (with respect to the latent design variables) using different optimization algorithms. The new non-dominated points obtained via the VAE representation were found and compared with the known attainable set, indicating that use of this new design representation can simultaneously improve computational efficiency and solution quality.

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