[Paper Review] Diffusion Models Beat GANs on Topology Optimization

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

Topology Optimization in Engineering21 citations

TL;DR

TopoDiff uses conditional diffusion models with regressor and classifier guidance to optimize topology for low compliance and manufacturability, outperforming a state-of-the-art conditional GAN across metrics.

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/.

Motivation & Objective

• Motivate topology optimization as essential for engineering design and identify limitations of GAN-based approaches (training difficulty, generalization, manufacturability).
• Propose a diffusion-model-based framework (TopoDiff) that incorporates performance and manufacturability guidance.
• Investigate whether conditional diffusion models can outperform GANs on TO under varied boundary conditions and constraints.
• Provide a general framework for applying diffusion models to engineering inverse problems with performance and feasibility constraints.

Proposed method

• Use a UNet-based conditional diffusion model with four input channels: volume fraction, strain energy density, von Mises stress, and boundary-boundary loads.
• Introduce regressor guidance via a surrogate model that predicts compliance and shifts the diffusion denoising mean to reduce high-compliance designs.
• Introduce classifier guidance to penalize floating material by incorporating a floating-material classifier into the sampling process.
• Combine regressor and classifier guidance with a controlled maximum noise level to steer samples toward feasible, low-compliance topologies (Algorithm 2).
• Represent constraints and boundary conditions as additional channels and use physical fields computed via finite element analysis to inform conditioning.

Experimental results

Research questions

• RQ1 Can conditional diffusion models outperform GANs in topology optimization with explicit performance and manufacturability guidance?
• RQ2 How can regressor (compliance) and classifier (feasibility) guidance be integrated into diffusion sampling for TO?
• RQ3 Do diffusion-based TO methods generalize to out-of-distribution boundary conditions and varied loads?

Key findings

• TopoDiff achieves an eight-times reduction in average compliance error compared to TopologyGAN on level-2 tests and an eleven-times reduction on level-1 tests.
• TopoDiff produces eleven-times fewer non-manufacturable designs (floating material) than the GAN baseline on level-1 data and about six-times fewer on level-2 data.
• Across level-1 tests, TopoDiff reduces average compliance error from 48.51% to 4.39% with guided sampling.
• Across level-2 tests, TopoDiff reduces average compliance error from 143.08% to 18.40% with guided sampling.
• Guided TopoDiff reduces average volume fraction error and substantially lowers the presence of floating material compared to TopologyGAN.
• Surrogate models for compliance and floating-material prediction remain reliable on low-noise inputs and degrade gracefully with higher noise.