Deep Generative Models for Topology Optimization

Topology optimization constitutes a powerful computational approach for devis- ing structures exhibiting optimized performance under designated constraints. In this thesis, we introduce a deep generative model, based on di↵usion models, to address the minimum compliance problem.

The minimum compliance problem entails the identification of an optimal mate- rial distribution within a prescribed design domain, such that structural sti↵ness is maximized or, equivalently, compliance—a metric gauging flexibility—is min- imized, subject to specific loading and boundary conditions.

Deep generative models represent a category of deep learning algorithms that have emerged as a propitious alternative to conventional topology optimiza- tion methodologies. These models, which encompass Variational Autoencoders (VAEs), Generative Adversarial Networks (GANs), and their variations, have demonstrated remarkable success in engendering high-quality designs through data-driven processes. Our research presents a successful framework based on the di↵usion model which outperforms GAN-based models.

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