Generative Adversarial Design Analysis of Non-Convexity in Topology Optimization

Abstract

Material penalization and filtering schemes are key strategies applied to topology optimization (TO) to promote more discrete and manufacturable designs. However, these modifications introduce fluctuations in the design landscape that amplify non-convexity and influence the local minima identified by TO. Harnessing the machine learning approach of generative adversarial networks (GAN), we investigate the role of penalization and filtering by comparing the designs between TO and GAN-based TO surrogates. A total of 17 GANs were constructed to predict 2D minimum compliance topologies across a set of penalization factors and filters, each interpolating a design space of 270,000 boundary condition and loading scenarios. The prevalence of GAN-predicted topologies with better compliance than TO-calculated topologies was estimated via a random sampling of the design space. GAN ‘over-performance’ occurs across material penalization and filtering conditions, where the frequency tends to increase as penalization increases. Analysis of this test set is leveraged to highlight trends regarding the conditions under which this ‘over-performance’ occurs, and the geometric characteristics these designs exhibit. Collectively, this study presents an alternative method to characterize the effects of penalization and filtering on design outcomes and motivates the use of data-driven surrogates to augment traditional approaches.