To Quantize or Not to Quantize: Effects on Generative Models for 2D Heat Sink Design

Abstract In Topology Optimization (TO) and related engineering applications, physics-constrained simulations are often used to optimize candidate designs given some set of boundary conditions. However, such models are computationally expensive and do not guarantee convergence to a desired result, given the frequent non-convexity of the performance objective. Creating data-based approaches to warm-start these models — or even replace them entirely — has thus been a top priority for researchers in this area of engineering design. In this paper, we present a new dataset of two-dimensional heat sink designs optimized via Multiphysics Topology Optimization (MTO). Further, we propose an augmented Vector-Quantized GAN (VQGAN) that allows for effective MTO data compression within a discrete latent space, known as a codebook, while preserving high reconstruction quality. 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, generating thermally performant heat sink designs within a fraction of the time taken by conventional optimization approaches. We show the transformer-based approach is more effective than using a Deep Convolutional GAN (DCGAN) due to its elimination of mode collapse issues, as well as better preservation of topological connections in MTO and similar applications.