[论文解读] Diffusion Models Beat GANs on Topology Optimization

François Mazé, Faez Ahmed|arXiv (Cornell University)|Aug 20, 2022

Topology Optimization in Engineering被引用 21

一句话总结

TopoDiff 使用带回归器和分类器引导的条件扩散模型来优化拓扑以实现低合规性和可制造性，在各项指标上优于最先进的条件GAN。

ABSTRACT

Structural topology optimization, which aims to find the optimal physical structure that maximizes mechanical performance, is vital in engineering design applications in aerospace, mechanical, and civil engineering. Generative adversarial networks (GANs) have recently emerged as a popular alternative to traditional iterative topology optimization methods. However, these models are often difficult to train, have limited generalizability, and due to their goal of mimicking optimal structures, neglect manufacturability and performance objectives like mechanical compliance. We propose TopoDiff - a conditional diffusion-model-based architecture to perform performance-aware and manufacturability-aware topology optimization that overcomes these issues. Our model introduces a surrogate model-based guidance strategy that actively favors structures with low compliance and good manufacturability. Our method significantly outperforms a state-of-art conditional GAN by reducing the average error on physical performance by a factor of eight and by producing eleven times fewer infeasible samples. By introducing diffusion models to topology optimization, we show that conditional diffusion models have the ability to outperform GANs in engineering design synthesis applications too. Our work also suggests a general framework for engineering optimization problems using diffusion models and external performance with constraint-aware guidance. We publicly share the data, code, and trained models here: https://decode.mit.edu/projects/topodiff/.

研究动机与目标

• 将拓扑优化作为工程设计的关键，并识别基于GAN的方法的局限性（训练难度、泛化性、可制造性）。
• 提出一个基于扩散模型的框架（TopoDiff），将性能和可制造性引导纳入其中。
• 研究条件扩散模型在边界条件和约束变化下是否能在拓扑优化中优于GAN。
• 提供一个将扩散模型应用于具有性能与可行性约束的工程反问题的一般框架。

提出的方法

• 使用基于UNet的条件扩散模型，具有四个输入通道：体积分数、应变能密度、冯·米塞应力以及边界-边界载荷。
• 通过预测合规性的代理模型引入回归器引导，并将扩散去噪均值偏移以降低高合规性设计。
• 引入分类器引导，通过在采样过程中加入浮动材料分类器来惩罚漂浮材料。
• 将回归器和分类器引导与受控的最大噪声水平相结合，以引导样本朝向可行的低合规拓扑（算法2）。
• 将约束和边界条件表示为附加通道，并使用通过有限元分析计算的物理场来为条件化提供信息。

实验结果

研究问题

• RQ1 在具有明确性能和可制造性引导的拓扑优化中，条件扩散模型是否能优于GAN？
• RQ2 回归器（合规性）和分类器（可行性）引导如何整合到拓扑优化的扩散采样中？
• RQ3 基于扩散的拓扑优化方法是否能泛化到分布外的边界条件和不同载荷？

主要发现

• TopoDiff 在 level-2 测试中相较于 TopologyGAN 在平均合规误差上降低八倍，在 level-1 测试中降低十一倍。
• TopoDiff 在 level-1 数据上产生的不可制造设计（浮动材料）比GAN基线少11倍，在 level-2 数据上约少6倍。
• 在 level-1 测试中，TopoDiff 通过引导采样将平均合规误差从 48.51% 降至 4.39%。
• 在 level-2 测试中，TopoDiff 通过引导采样将平均合规误差从 143.08% 降至 18.40%。
• 引导的 TopoDiff 相较于 TopologyGAN，在平均体积分数误差上有所降低，并显著减少浮动材料的存在。
• 合规性和浮动材料预测的代理模型在低噪声输入下仍然可靠，并在更高噪声下优雅降解。