To Quantize or Not to Quantize: Effects on Generative Models for Topology Optimization Problems

Abstract In Topology Optimization (TO) and related engineering applications, physics-constrained simulations are often used to optimize candidate designs given some set of design conditions. Such models can be computationally expensive and do not guarantee convergence to a desired result, given the frequent non-convexity of design optimization problems. Creating data-driven approaches to warm-start these models—or even replace them entirely—has thus been an active area for engineering design researchers. In this paper, we propose an augmented Vector-Quantized GAN (VQGAN) that allows for effective compression of TO designs within a discrete latent space, known as a codebook, while preserving high reconstruction quality. Further, we present a new dataset of two-dimensional heat sink designs optimized via Multiphysics Topology Optimization (MTO) to train and evaluate this model. To concretely assess the benefits of the VQGAN quantization process, we conduct a latent analysis of its codebook as compared to the continuous latent space of a deep autoencoder (AE). We find that VQGAN can more effectively learn topological connections despite a high rate of data compression. Finally, we leverage the VQGAN codebook to train a small GPT-2 model that is capable of rapid generation of thermally performant heat sink designs. We show that the transformer-based approach is more effective than using a Wasserstein GAN with Gradient Penalty (WGAN-GP) due to its superior preservation of topological connections in MTO and similar applications.