Session: 13-19-02: Scientific Machine Learning (SciML) for Characterization, Modeling, and Design of Structures and Materials II

Paper Number: 166864

Latent Space Diffusion Models With Auxiliary Losses for Structural Topology Optimization 

Topology optimization is a crucial process in structural design which aims to optimize the material distribution in a predefined domain subject to various conditions, such as thermal or structural loading. The limitations of gradient methods to structural topology optimization, such as long sampling time and computational complexity, have prompted recent studies into the use of image based machine learning algorithms for topology optimization [1, 2]. Consequently, this project addresses these challenges by leveraging a class of image generation models, latent diffusion models [3] (LDMs). LDMs leverage latent space representations to perform conditional image generation more efficiently than traditional diffusion models, making them well-suited for the task of topology optimization. We propose a framework that conditions LDMs with pre-calculated stress and strain information to generate informed structural designs. We integrate a variational autoencoder (VAE) into our LDM framework, trained with the auxiliary objectives of reducing floating material, matching the input volume fraction, and reducing load discrepancies. This approach, using auxiliary losses to penalize the VAE, ensures that the latent space encoding accurately maps to designs with the physical properties and expectations of the optimized structure. The VAE framework is organized into two pipelines, encoding structural designs and contextual conditions separately to ensure latent topology vectors are independent from the input conditions of the design. The LDM is then able to learn the mapping from input conditions onto the latent design space. Because the latent domain is already pre-conditioned to abide by the physical properties, the LDM has less computational overhead, effectively splitting the learning process between two stages. Our experimental evaluation demonstrates that the proposed VAE-LDM approach achieves competitive compliance performance compared to state-of-the-art methods such as TopoDiff [1]. Experimental results demonstrate that the VAE-LDM approach achieves competitive performance, with a compliance error of 3.45%, outperforming the state-of-the-art TopoDiff model, which achieves a compliance error of 4.39%. These results highlight the potential of LDMs to provide efficient, flexible, and scalable solutions for topology optimization problems. Our framework can be further developed to adapt to 3D topology optimization schemes, non-square design domains, dynamic optimization problems, or conditional optimization problems, such as additive manufacturing constraints.

[1] Mazé, François, and Faez Ahmed. 2022. “Diffusion Models Beat GANs on Topology Optimization.” arXiv.
[2] Nie, Zhenguo, Tong Lin, Haoliang Jiang, and Levent Burak Kara. 2021. “TopologyGAN: Topology Optimization Using Generative Adversarial Networks Based on Physical Fields Over the Initial Domain.” Journal of Mechanical Design 143 (031715).
[3] Rombach, Robin, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Björn Ommer. 2022. “High-Resolution Image Synthesis with Latent Diffusion Models.

Presenting Author: Aaron Lutheran University of North Carolina at Charlotte

Presenting Author Biography: Aaron Lutheran is a PhD student at the University of North Carolina at Charlotte, specializing in machine learning for design optimization. He holds a Master's degree in Mechanical Engineering from UNC Charlotte, where he developed a strong foundation in advanced computational engineering principles. Aaron is deeply involved in research, working as a research assistant for the university in collaboration with Corvid Technologies. His research focuses on the application of machine learning techniques to solve complex optimization problems.

Authors:

Aaron Lutheran University of North Carolina at Charlotte
Srijan Das University of North Carolina at Charlotte
Alireza Tabarraei University of North Carolina at Charlotte