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Optimize Any Topology: A Foundation Model for Shape- and Resolution-Free Structural Topology Optimization
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Introduces Optimize Any Topology (OAT), a resolution- and shape-agnostic latent diffusion foundation model for minimum-compliance topology optimization, trained on the new 2.2M-sample OpenTO dataset.
Problem
Existing deep-learning topology optimization models are limited to fixed square grids, a small set of boundary conditions and single loads, and generalize poorly to arbitrary shapes, resolutions, and loads.
Approach
A resolution-free autoencoder with an implicit neural-field (convolutional local image function) decoder maps topologies to fixed-size latents, and a conditional latent diffusion model (velocity parameterization, classifier-free guidance) is conditioned on BPOM point-cloud embeddings of loads/supports plus volume fraction, cell size, and aspect ratio, trained on a randomly generated dataset.
Key results
- On the 64x64 benchmark OAT reaches 1.74% mean compliance error without optimization vs 2.59% for the best prior model (TopoDiff w/ guidance), and 0.0503% with 10 SIMP refinement steps.
- On the fully random OpenTO benchmark OAT achieves 8.17% mean CE on non-failure samples, below NITO's 13.14%, though with a 39.22% failure rate vs NITO's 60.01%.
- OAT generates a 64x64 sample in 0.508 s and a 256x256 sample in 0.51 s on an RTX 4090, nearly constant with resolution, while NITO-L scales from 0.05 s to 0.67 s.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use OAT instead of TopoDiff w/ G | 64 x 64 topology optimization · 64 x 64 benchmark | CE %: 2.59 -> 1.74 | Helped |
| Use OAT instead of NITO | 256 x 256 topology optimization · 256 x 256 benchmark | CE %: 9.178 -> 1.51 | Helped |
| Use OAT instead of NITO | OpenTO fully general benchmark · OpenTO fully general benchmark, non-failure samples | CE* %: 13.14 -> 8.17 | Helped |
| Use OAT instead of NITO | OpenTO fully general benchmark · OpenTO fully general benchmark | Failure Rate %: 60.01 -> 39.22 | Helped |
| Add 5 steps of post-generation optimization | OAT · OpenTO fully general benchmark | Failure Rate %: 39.22 -> 22.11 | Helped |
| Add 10 steps of post-generation optimization | OAT · OpenTO fully general benchmark | CE* %: 8.17 -> 4.31 | Helped |
| Increase the number of generated candidates and select the best of 8 | OAT · OpenTO fully general benchmark | Failure Rate %: 39.22 -> 21.50 | Helped |
| Use DDIM rather than DDPM sampling (ablation) | OAT sampling · OpenTO benchmark | CE and VFE | Mixed |
| Use 20 rather than 40 denoising steps (ablation) | OAT DDIM sampling · OpenTO benchmark | CE and VFE | Helped |
| Set classifier-free guidance scale to 2 (ablation) | OAT DDIM sampling · OpenTO benchmark | VFE | Helped |
| Increase guidance scale from 1 to 2 (ablation) | OAT DDIM sampling · OpenTO benchmark | CE | No clear effect |
| Reconstruct out-of-distribution heatsink topologies with OAT's autoencoder without retraining | OAT autoencoder · heatsink optimized topologies | IoU: 0.94 IoU | Helped |
Surprising findings
- Best-of-64 sampling drops the OpenTO failure rate to 11.51% and mean CE on non-failure samples to 0.44%.
- Without any post-generation optimization, OAT already matches or beats specialized models on the 64x64 benchmark that use direct optimization for some settings.
Limitations
- High failure rate (about 39%) on the fully random OpenTO benchmark without refinement.
- Limited to 2D minimum-compliance under linear elasticity; does not cover stress or buckling constraints.
- NITO baseline trained with a variant at matched parameter count, and OpenTO test set is authors' own construction.
Experimental setup
Datasets: OpenTO 64x64 TopoDiff benchmark data (194,000 samples) 256x256 NITO benchmark data
Benchmarks: 64x64 benchmark 256x256 benchmark five-shape benchmark OpenTO general benchmark
Metrics: compliance error (mean) compliance error (median) volume fraction error failure rate inference time
Baselines: TopologyGAN cDDPM TopoDiff DOM NITO
Builds on: Latent Diffusion Models INFD BPOM NITO TopoDiff SIMP
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