TopoCtrl: Post-Optimization Topology Editing Toward Target Structural Characteristics

Abstract

Topology optimization can generate high-performance structures, but designers often need to revise the resulting topology in ways that reflect fabrication preferences, structural intuition, or downstream design constraints. In particular, they may wish to explicitly control interpretable structural characteristics such as member thickness, characteristic member length, the number of joints, or the number of members connected to a joint. These quantities are often discrete, non-smooth, or only available through a forward evaluation procedure, making them difficult to impose within conventional optimization pipelines. We present TopoCtrl, a post-optimization control framework that repurposes the latent space of a pre-trained topology foundation model for explicit characteristic-guided editing. Given an optimized topology, TopoCtrl encodes it into the latent space of a latent diffusion model, applies partial noising to preserve instance similarity while creating room for modification, and then performs regression-guided denoising toward a prescribed target characteristic. The concept is to train a lightweight regression model on latent representations annotated with evaluated structural characteristics, and to use its gradient as a differentiable guidance signal during reverse diffusion. This avoids the need for characteristic-specific reformulations, hand-derived sensitivities, or iterative optimization. Because the method operates through partial noising of an existing topology latent, it preserves overall structural similarity while still enabling characteristic controls. Across representative control tasks involving both continuous and discrete structural characteristics, TopoCtrl produces target-aligned topology modifications while better preserving structural coherence and design intent than indirect parameter tuning or naive geometric post-processing.

Figures (15)

• Figure 1: TopoCtrl uses a pretrained OAT with frozen weights. Given a reference topology and a user-specified target characteristic (number of joints, maximum members connected to a joint, maximum member length, and member thickness), TopoCtrl encodes the input into OAT’s structured latent, applies partial noising. A small regression model is trained on a small dataset of latent-characteristic pairs to predict the target characteristic. Starting from the noisy latent, we perform diffusion denoising with regression-model guidance toward the target characteristic to recover an edited clean latent that preserves structural similarity. Finally, the edited latent is decoded to yield the edited topology with characteristics matching the target.
• Figure 2: An overview of the OAT framework. First, an autoencoder is trained which the encoder encodes problems of arbitrary shapes into a structured fixed resolution latent $z_0$ and the decoder decodes it back to the original topology. Given the problem configuration in the design domain, the problem embedding $P$ is fed into the diffusion model as a conditioning vector. The output from the latent diffusion model is a fixed-resolution latent, which the decoder decodes into a topology.
• Figure 3: The characteristic distributions of the filtered 150K-sample training dataset used for regression model training. We show the four quantities used in TopoCtrl: the number of joints, the maximum number of members incident to a joint, the normalized average of the top two longest members, and the normalized 90th-percentile thickness. The dataset is moderately imbalanced, with joint counts concentrated toward the lower end, most joint complexities lying between 3 and 5, characteristic length concentrated around intermediate values, and thickness spread more broadly across the range.
• Figure 4: Prediction performance of the latent-space regression models on the testing set. Each plot compares the ground-truth characteristic computed from the topology against the value predicted from the latent representation. The regressors recover the main trend of each characteristic. The continuous quantities, namely characteristic length and thickness, exhibit smoother prediction behavior, while the discrete quantities, such as joint count and maximum joint complexity, are more challenging near the tails of the distribution. The length prediction showed slightly higher error around the lower and higher ends of the characteristic values. This also caused the subsequent slight increase in error with the length control evaluations.
• Figure 5: Characteristic control accuracy of TopoCtrl over the 100 test topologies using best-of-64 sampling. For the discrete-valued characteristics: the number of joints and the maximum number of members incident to a joint, we use swarm plots. For the continuous-valued characteristics: the normalized characteristic length and normalized 90th-percentile thickness, we use violin plots. In each case, the selected result is the sample whose evaluated characteristic is closest to the requested target under the same medial-axis-based analysis used for dataset annotation. TopoCtrl achieves good target accuracy, with somewhat reduced precision at more extreme target values.