De-homogenization using convolutional neural networks

This paper presents a deep learning-based de-homogenization method for structural compliance minimization. By using convolutional neural network to parameterize the mapping from set of lamination parameters on coarse mesh one-scale design fine mesh, we avoid solving least square problems associated with traditional approaches and save time correspondingly. To train network, two-step custom loss function has been developed which ensures periodic output field that follows local orientations. A key feature proposed is training carried out without any use or reference underlying optimization problem, renders robust insensitive wrt. domain size, boundary conditions, loading. post-processing procedure utilizing distance transform skeleton used project desired widths onto while ensuring predefined minimum length-scale volume fraction. demonstrate learning approach excellent generalization properties, numerical examples are shown several different load conditions. For an appropriate choice parameters, de-homogenized designs perform within $7-25\%$ homogenization-based solution at fraction computational cost. With options further improvements, scheme may provide basis future interactive high-resolution topology optimization.