Optimize Any Topology: A Foundation Model for Shape- and Resolution-Free Structural Topology Optimization

TL;DR

Optimize Any Topology (OAT) presents a foundation-model approach to topology optimization that is agnostic to domain shape, aspect ratio, and resolution. It combines a resolution-free autoencoder with an implicit neural-field decoder and a conditional latent-diffusion model trained on the OpenTO dataset, enabling sub-second inference and generalization across diverse TO problems. The OpenTO dataset (2.194M samples) provides a large-scale, randomized corpus to train physics-aware generative models for inverse design, while OAT achieves up to an order of magnitude improvement in mean compliance error over prior methods on canonical benchmarks and generalizes to fully random problem configurations. This work demonstrates the viability of diffusion-based foundation models for real-time, physics-driven design exploration and introduces a resource for further research in generative modeling for inverse design in TO and related multi-physics domains.

Abstract

Structural topology optimization (TO) is central to engineering design but remains computationally intensive due to complex physics and hard constraints. Existing deep-learning methods are limited to fixed square grids, a few hand-coded boundary conditions, and post-hoc optimization, preventing general deployment. We introduce Optimize Any Topology (OAT), a foundation-model framework that directly predicts minimum-compliance layouts for arbitrary aspect ratios, resolutions, volume fractions, loads, and fixtures. OAT combines a resolution- and shape-agnostic autoencoder with an implicit neural-field decoder and a conditional latent-diffusion model trained on OpenTO, a new corpus of 2.2 million optimized structures covering 2 million unique boundary-condition configurations. On four public benchmarks and two challenging unseen tests, OAT lowers mean compliance up to 90% relative to the best prior models and delivers sub-1 second inference on a single GPU across resolutions from 64 x 64 to 256 x 256 and aspect ratios as high as 10:1. These results establish OAT as a general, fast, and resolution-free framework for physics-aware topology optimization and provide a large-scale dataset to spur further research in generative modeling for inverse design. Code & data can be found at https://github.com/ahnobari/OptimizeAnyTopology.

Figures (25)

• Figure 1: In TO, the objective is to distribute material in a domain (a density field $\rho(x)$) to obtain optimal physics-based performance. Above, we show an example of TO for maximum stiffness, given boundary conditions of material supports and forces applied.
• Figure 2: OAT generative framework overview. A resolution-free autoencoder encodes variable OpenTO dataset topologies into a fixed-resolution latent space. Latent diffusion models (LDMs) then conditionally generate topologies. Problem specifications, including forces and boundary conditions represented as point clouds, are processed by BPOM models and MLPs to form a fixed-size embedding to condition the LDM.
• Figure 3: Left: Samples from ground truth (top), NITO (middle), and OAT (bottom) on a random OpenTO benchmark; compliance errors shown below. NITO outputs are noisy with many gray pixels, unsuitable for real-world use. Right: Example highlighting sensitivity in TO; slight deviations by OAT led to material misplacement at boundary conditions, causing design failure. This highlights the precision requirements of TO.
• Figure 4: Top: Results of ablation studies on denoising steps. Observe that despite CE being lower in DDPM sampling, this is largely due to DDPM sampling using significantly more material, as evidenced by the much higher VFE values. Bottom: Ablation on the guidance scale shows that CE largely stays the same for the guidance scale of 1 and 2, while VFE is optimal at a guidance scale of 2.0.
• Figure 5: Heatsink optimized topologies reconstructed using OAT's auto-encoder without any additional training. This demonstrates OAT's zero-shot capability to extend to different physics and TO problems with relative ease.