TopologyGAN: Topology Optimization Using Generative Adversarial Networks Based on Physical Fields Over the Initial Domain

Abstract

In topology optimization using deep learning, the load and boundary conditions represented as vectors or sparse matrices often miss the opportunity to encode a rich view of the design problem, leading to less than ideal generalization results. We propose a new data-driven topology optimization model called TopologyGAN that takes advantage of various physical fields computed on the original, unoptimized material domain, as inputs to the generator of a conditional generative adversarial network (cGAN). Compared to a baseline cGAN, TopologyGAN achieves a nearly 3 × reduction in the mean squared error and a 2.5 × reduction in the mean absolute error on test problems involving previously unseen boundary conditions. Built on several existing network models, we also introduce a hybrid network called U-SE(Squeeze-and-Excitation)-ResNet for the generator that further increases the overall accuracy. We publicly share our full implementation and trained network.

A Study on Using Image-Based Machine Learning Methods to Develop Surrogate Models of Stamp Forming Simulations

“…Other IBMLM models using U-Nets [42][43][44] are not be described at length in this paper. The Res-SE blocks discussed above have been combined with U-Nets in several studies [14,45,46]. A remarkable increase in accuracy was observed using these Res-SE-U-Nets.…”

Rapid feasibility assessment of components to be formed through hot stamping: A deep learning approach

“…A Res-SE-U-Net was selected in this paper to serve as the CNN architecture. Res-SE-U-Nets have recently been proven to be effective architectures for image-to-image translation tasks by a number of studies [17,25,30]. This novel architecture consists of two key components: a U-Net backbone with concatenative skip connections and integrated ResNet layers with Squeeze and Excitation modules (Res-SE) (detailed in Figure 15).…”

“…To overcome the aforementioned limitations, researchers have recently borrowed modelling techniques from the field of deep learning, a subset of machine learning. In particular, Convolutional Neural Networks (CNNs), in conjunction with image representations of design inputs and computer simulation results outputs have been employed to preserve prediction informativeness without a mesh based dependency [17,[23][24][25][26][27][28][29]. CNNs are a particular class of neural networks that have gained popularity when working with spatially structured data such as grids or images.…”

Data-driven topology design using a deep generative model

“…Because MMC can represent structural shape and topology with a small number of design variables, it is expected that the computational cost for learning is reduced. As a related study of Zhang et al (2019b), Nie et al (2020) proposed the utilization of stress and strain energy density fields of the initial material distributions as the input data. In their study, a conditional generative adversarial network (cGAN) (Mirza and Osindero 2014) is used to improve computational efficiency.…”