Latent Space Diffusion for Topology Optimization

2025-08-07

AI Summary

To address the high computational cost of gradient-based methods in high-resolution, high-dimensional topology optimization, this paper proposes a physics-guided generative framework. First, a variational autoencoder (VAE) compresses structural topologies into a low-dimensional latent space. Then, a conditional latent diffusion model is constructed, where dense physical fields—including von Mises stress and strain energy density—serve as conditioning inputs; a multi-task loss function further enforces constraints on floating material, load equilibrium, and volume deviation. This end-to-end approach significantly improves the physical plausibility, manufacturability, and connectivity of generated designs. Evaluated on a large-scale synthetic dataset, the method outperforms existing diffusion-based approaches in compliance accuracy, robustness of volume control, and scalability—demonstrating superior generalization and efficiency for complex topology optimization tasks.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems

Abstract

Topology optimization enables the automated design of efficient structures by optimally distributing material within a defined domain. However, traditional gradient-based methods often scale poorly with increasing resolution and dimensionality due to the need for repeated finite element analyses and sensitivity evaluations. In this work, we propose a novel framework that combines latent diffusion models (LDMs) with variational autoencoders (VAEs) to enable fast, conditional generation of optimized topologies. Unlike prior approaches, our method conditions the generative process on physically meaningful fields, specifically von Mises stress, strain energy density, volume fraction, and loading information, embedded as dense input channels. To further guide the generation process, we introduce auxiliary loss functions that penalize floating material, load imbalance, and volume fraction deviation, thereby encouraging physically realistic and manufacturable designs. Numerical experiments on a large synthetic dataset demonstrate that our VAE-LDM framework outperforms existing diffusion-based methods in compliance accuracy, volume control, and structural connectivity, providing a robust and scalable alternative to conventional

Problem

• Efficient topology optimization at high resolution
• Reducing computational cost of gradient-based methods
• Generating physically realistic manufacturable designs

Innovation

• Combines latent diffusion models with VAEs
• Conditions generation on physical stress fields
• Uses auxiliary losses for manufacturable designs