TopoEdit: Fast Post-Optimization Editing of Topology Optimized Structures

Hongrui Chen; Josephine V. Carstensen; Faez Ahmed

cs.GRFeb 25, 2026

TopoEdit: Fast Post-Optimization Editing of Topology Optimized Structures

Authors: Hongrui Chen, Josephine V. Carstensen, Faez Ahmed

Organizations: Massachusetts Institute of Technology, Cambridge, MA, 02139

Abstract

Despite topology optimization producing high-performance structures, late-stage localized revisions remain brittle: direct density-space edits (e.g., warping pixels, inserting holes, swapping infill) can sever load paths and sharply degrade compliance, while re-running optimization is slow and may drift toward a qualitatively different design. We present TopoEdit, a fast post-optimization editor that demonstrates how structured latent embeddings from a pre-trained topology foundation model (OAT) can be repurposed as an interface for physics-aware engineering edits. Given an optimized topology, TopoEdit encodes it into OAT's spatial latent, applies partial noising to preserve instance identity while increasing editability, and injects user intent through an edit-then-denoise diffusion pipeline. We instantiate three edit operators: drag-based topology warping with boundary-condition-consistent conditioning updates, shell-infill lattice replacement using a lattice-anchored reference latent with updated volume-fraction conditioning, and late-stage no-design region enforcement via masked latent overwrite followed by diffusion-based recovery. A consistency-preserving guided DDIM procedure localizes changes while allowing global structural adaptation; multiple candidates can be sampled and selected using a compliance-aware criterion, with optional short SIMP refinement for warps. Across diverse case studies and large edit sweeps, TopoEdit produces intention-aligned modifications that better preserve mechanical performance and avoid catastrophic failure modes compared to direct density-space edits, while generating edited candidates in sub-second diffusion time per sample.

Figures & tables

Figure 1: TopoEdit uses a pretrained OAT with frozen weights. Given a reference topology and a user-specified desired edit (topology warp, lattice infill replacement, or no-design region enforcement), TopoEdit encodes the input into OAT’s structured latent, applies partial noising, and converts the edit into a corresponding latent-space intervention to produce an edited initialization. Starting from the edited latent, we run diffusion denoising with consistency-preserving guidance to recover an edited clean latent that preserves the instance identity away from the edit while allowing localized structural adaptation. Finally, the edited latent is decoded to yield the edited topology.

Parameter	Warp	Lattice	No Design
DDIM Total Steps ( $t_{total}$ )	100	200	100
DDIM Partial Steps ( $\tau$ )	20	20	25
Guidance Step Size ( $s$ )	1000	1000	1000

Table 1: Hyperparameter configuration for the three topology editing tasks. The ratio between partial

\tau

and total steps

t_{total}

determines the noise level added to the latent vector. For lattice infill, we use a smaller partial-noise ratio

\tau/t_{total}

to keep denoising in a refinement regime that preserves the reference lattice’s periodic member layout while permitting small boundary condition-aware corrections.

Panel of Figure 2 — Figure 2: Illustration of a warp edit. A green handle point is selected on the topology, and a red arrow represents a warp vector. The vector’s magnitude determines the target’s location (red cross), indicating the handle point’s movement. The percentage difference in distance between the green point and the target location is calcualted Distance Error (DE). Additionally, the Compliance Error (CE) can be computed. (b) Direct warp: When the warp is performed directly on the topology, the edit causes significant local deformation, while the distance error remains relatively small. However, the compliance error increases as straight members become distorted. SIMP post-processing partially reverts some of the local changes, which reduces the distance error. Latent warp: In this case, the edit is reflected on the global topology, where post-processing has not made substantial changes to the topology. As a result, the topology remains stable, and the distance error is smaller.

Figure 3: TopoEdit workflow for warping the topology. The topology is first converted into latent $z_{0}$ , then partial noise is added $z_{\tau}$ , then the warp operation is mapped onto the latent space $z_{\tau}^{\prime}$ , then the warped latent is denoised to obtain the latent $z_{0}^{\prime}$ . Decoding $z_{0}^{\prime}$ gives the edited topology.

Panel of Figure 4 — Figure 4: We select examples from the warp experiments to visualize the direct and latent-based edit. All edit results shown are after 10 steps of SIMP post-processing. The last three example is from the testing set. Left column: the reference topology. The warp edit is placed on a joint and shown as a red arrow with the end located at the point where the warp is applied and the arrow head pointing towards the target edit direction. Middle column: applying the warp edit directly to the topology, after SIMP post-processing, a larger deviation from the reference topology occurs. We show the closest joint point to the target edit location as a green dot and the edit target location as a red cross. In cases with large changes in topology after post-processing, the closest joint location is located on a different edge completely. The abrupt changes caused by the direct warp cause the post-processing optimizer to alter the topology and connectivity. Right column: with latent-based warp edits, the overall appearance of the structure is better preserved, resulting in smaller error compliance and a closer distance to the target location.

Panel of Figure 5 — Figure 5: Applying the edit (a), direct warp (b) is deterministic and produces a single result. Latent warp (c) based on the diffusion model is stochastic; the same edit on the latent can produce different results. The number of results generated can be selected as one of the configuration parameters. The stochastic nature of the diffusion model allows the user to explore a distribution of possible outcomes.

Panel of Figure 6 — Figure 6: We compute the distribution of the direct and latent warp (best of 64) across all warp operations for both the training and the testing set. For this plot, we apply a failure cutoff and drop cases where the compliance exceeds 1000% of the original topology, since these cases typically correspond to broken load transfer and dominate aggregate statistics. The distribution is visualized using seaborn contours. Initially, without any post-processing (step 0), the latent warp achieved a smaller compliance error but with a slightly larger error in distance. As more steps of post-processing are applied, we observe that the center of the latent warp remains consistent, indicating that the latent warp successfully performed a more global edit. Post-processing primarily reduced the spread of the warp. In contrast, the direct warp shifted towards the right, suggesting that the local edit was reversed.

Table 2: The best of N performance for the testing set. We see the same trend with the seaborn contour plot. The failure rate is evaluated as an edited result with more than 100% compliance with the original structure.

Figure 7: TopoEdit workflow for lattice replacement. We take an existing topology and then apply lattice infill into it. The topology is first converted into latent $z_{0}$ , then partial noise is added $z_{\tau}$ , then the noised latent is denoised to obtain the latent $z_{0}^{\prime}$ . Decoding $z_{0}^{\prime}$ gives the topology with lattice infill.

Panel of Figure 8 — Figure 8: We visualize the result of direct and latent-based lattice replacement. The third and last row is from the testing set. (a) The original reference topology with boundary condition overlaid in blue and the compliance value. (b) The first three rows are using a grid-shaped lattice, and the last three rows are a cross-shaped lattice. When directly replacing the internal structure with lattices, the potential of missing a boundary condition is high, resulting in exploding compliance values. (c) With latent-based edits, the overall appearance of the lattice structure is preserved, while OAT managed to nudge the lattice structure to cover boundary condition points and align with the load paths. Resulting in lower compliance while still maintaining an acceptable IoU score to the original latent-replaced structures.

Table 3: Best of N result for the lattice replacement with the testing set. The beat rate is defined as the lattice having smaller compliance than the direct replacement. Due to the dramatic change of volume fraction and chances of missing boundary conditions, we define the failure rate here as the edited topology having 1000 times the compliance as the original structure.

Figure 9: TopoEdit workflow with no design region enforcement. The topology is first converted into latent $z_{0}$ , then partial noise is added $z_{\tau}$ , then the no design region is mapped as a mask onto the latent space $z_{\tau}^{\prime}$ , then the masked latent is denoised to obtain the latent $z_{0}^{\prime}$ . Decoding $z_{0}^{\prime}$ gives the edited topology.

Panel of Figure 10 — Figure 10: We visualize the result of directly applying the circular no design region onto the topology versus applying it in the latent vector. The last row is selected from the testing set. (a) The original reference topology with boundary condition overlaid in blue and the compliance value. (b) With the no design region directly applied to joint points, the hole masks out important load paths on the topology, causing the compliance to dramatically increase. (c) In contrast, latent-based editing managed to route around the holes and significantly reduce the compliance compared to directly applying the no design region in (b).

Best of	VFE%	Violation%	Beat Rate%	Failure Rate%
2	-1.07	4.90	81.25	12.50
4	-1.33	4.93	87.50	6.25
8	-0.47	5.08	93.75	6.25
16	-0.67	4.69	100.00	0.00
32	-0.63	4.60	100.00	0.00
64	0.06	5.37	100.00	0.00

Table 4: Best of N result for the no design region with the testing set. We define the beat rate as latent based no design region enforcement having smaller compliance than directly applying the no design region onto the topology. We define the failure rate as the edited topology having 1000 times the compliance as the original structure.

Figure 11: Multiple warp operations can occur simultaneously. We apply two warp operations on the topology from the testing set (left), with the latent-based warp result shown on the right after 10 steps of post-processing. The compliance error is 26%, and the distance error is 27%. The higher compliance error could be due to the two edit operations causing greater changes for the topology and moving it away from the compliance optima.

Figure 12: Applying all three types of edit on a single example (left). We apply the topology warp and no design region first (middle), then apply the grid-shaped lattice infill replacement (right). The compliance of the original structure is 3.9, the middle structure is 4.12 and the lattice replaced structure is 5.74. The distance error is 43% and 36%.

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Yongmin Kwon, Namwoo Kang

Cho Chun Shik Graduate School of Mobility, Korea Advanced Institute of Science and Technology, 193 Munji-ro, Yuseong-gu, Daejeon, 34051, Republic of Korea · AI Research Team, Narnia Labs, 193 Munji-ro, Yuseong-gu, Daejeon, 34051, Republic of Korea

Topology Optimization Structural Mechanics Structural Engineering

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Mar 26, 2026

Large Language Models as Optimization Controllers: Adaptive Continuation for SIMP Topology Optimization

We present a framework in which a large language model (LLM) acts as an online adaptive controller for SIMP topology optimization, replacing conventional fixed-schedule continuation with real-time, state-conditioned parameter decisions. At every

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current compliance, grayness index, stagnation counter, checkerboard measure, volume fraction, and budget consumption

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and outputs numerical values for the penalization exponent

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on three 2-D problems (cantilever, MBB beam, L-bracket) at

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not the schedule geometry

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Shaoliang Yang, Jun Wang, Yunsheng Wang

Department of Mechanical Engineering, Santa Clara University, Santa Clara, CA 95053, USA

Topology Optimization Large Language Model-Guided Optimization Language Model-Based Control

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May 20, 2026

TO-Agents: A Multi-Agent AI Pipeline for Preference-Guided Topology Optimization

Topology optimization can generate efficient structures, but designers often must manually translate qualitative intent, such as desired visual style, product experience, or manufacturability into solver settings that are not directly tied to those preferences. We present TO-Agents, a multi-agent AI framework that connects natural-language design intent with iterative topology optimization. The framework converts a human-provided problem description into validated solver inputs, runs a topology optimization solver, renders the resulting 3D topology, and uses multi-view vision-language reasoning with an independent judge agent to critique each result and revise solver parameters. We evaluate the framework on two long-horizon design tasks: a cantilever beam benchmark and a phone-stand product design. In both tasks, the designer specifies an aesthetic preference for hierarchically branched structures inspired by natural tree morphologies, and the system performs four revision cycles across ten independent replicates. TO-Agents produces at least one preference-aligned design in 60% of trials for each case study, corresponding to up to 6x more successful trials than an ablated pipeline without visual or historical feedback. Judge scores and human evaluations show that the pipeline can identify effective parameter levers, recover from poor revisions, and expand design exploration. A manufacturing agent further post-processes top-ranked designs for additive manufacturing, enabling end-to-end intent-to-prototype design. We also identify failure modes, including overshooting, selective memory, misplaced tools, and incorrect parameter reasoning. These results suggest that agentic topology optimization can shift designers from low-level parameter tuning toward higher-level specification of form and function, while highlighting safeguards needed for reliable autonomous engineering design.

Isabella A. Stewart, Hongrui Chen, Faez Ahmed

Department of Civil and Environmental Engineering Massachusetts Institute of Technology Cambridge, MA, 02139 USA · Department of Mechanical Engineering Massachusetts Institute of Technology Cambridge, MA, 02139 USA

Topology Optimization Multi-Agent System Optimization Multi-Agent Collaboration Tool-Using Vision-Language Agents Preference Optimization Natural Language to Optimization Modeling

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Abstract

Topology Optimization

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