Learn to learn: Application to topology optimization

The objective of this article is to propose a new algorithm for topology optimization (TO), specifically in the context of additive manufacturing (AM). TO as a part design mechanism is particularly synergestic with AM. We propose to solve the TO problem using a pretrained deep neural network (DNN). We develop a variation of DNN architecture that has been used successfully in image processing, and its adaptation to TO problems constitutes the main focus of our work. We use a deep convolutional neural network to learn end-to-end mapping from the initial designs obtained by running solid isotropic material with penalization (SIMP) for a few iterations to the final optimal designs obtained when SIMP runs to convergence. The iterative updates from the initial designs to the converged ones is replaced by forward propagation through the trained DNN. Our approach can be thought of as a way to the develop a trained DNN that can imitate the gradient descent method used in the standard SIMP method. We present computational results that demonstrate that our approach can compete favorably with SIMP.