Comparative study on manifold learning approaches for parametric topology optimization problem via unsupervised deep learning

The study designs iterative and non-iterative network frameworks that can predict solutions for topology optimization. The modified solid isotropic material with the penalization method is applied for topology optimization and is used to generate the input and output of the network. The optimal solution was predicted with respect to the variation in the cross-sectional thickness of the considered structure. The network frameworks were constructed using various neural network architectures, that is, convolutional autoencoders, convolutional neural networks, and artificial neural networks. Herein, the structure is defined as a subdomain to improve training efficiency and parameterization. The density distribution and strain energy of the structure were expressed as reduced data using a convolutional autoencoder. Two numerical examples were considered to evaluate the accuracy and efficiency of the proposed network frameworks. The test data were constructed to evaluate the performance of the proposed network framework. It was confirmed that the non-iterative network framework shows a more benign performance than the iterative one.