Title: Optimize Any Topology: A Foundation Model for Shape- and Resolution-Free Structural Topology Optimization
Venue: NeurIPS 2025
Accepted: yes
Keywords: Topology Optimization

Diffusion Models

Deep Generative Models
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 × 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.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduced Optimiza Any Topology (OAT), a foundation model for structural topology optimization (TO) with linear elasticity, together with OpenTO, a new, large-scale dataset with $2.2 \\times 10^6$ optimized solutions\nacross $2 \\times 10^6$ unique boundary conditions (BCs). OAT is shown to outperform previous deep learning methods for TO on multiple datasets and is the first generative model to be able to generate solutions for a wide range \nof resolutions, aspect ratios, loads, and fixture configurations.\n\nOAT is a latent diffusion model with a neural field decoder that can handle arbitrary resolution outputs, a significant limitation of previous methods like Topodiff. A conditional diffusion model generates variable geometries in \nlatent space, the problem specifications are encoded using MLPs and Boundary Point Order-invariant MLPs (BPOMs) for point-cloud representations of forces and fixtures.\n\nOn multiple benchmarks, OAT demonstrates state of the art (SoTA) performance, reducing the compliance error compared to the numerical baseline method (SIMP) by up to $90\\%$ compared with previous models and maintains fast inference times on a single GPU.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths\n- OpenTO is a new TO training dataset with a diverse set of loading conditions, applied forces, and prescribed volumes.\n- OAT is, because it is trained on OpenTO, able to handle a diverse range of BCs/forces.\n- A comparison against both SoTA data-driven models (Topodiff, ...) and the standard numerical method (SIMP).\n- Tests of OOD problems and documentation of failure cases. \n- Paper is well written: Clear structure, good overview, Figure, good Tables\n\n## Weaknesess\n- My fundamental criticism: While the results of OAT compared with earlier models like TopoDiff are definitely impressive and a clear step forward, I believe the term \"foundation model\" is overclaiming. OAT only applies to linear elasticity problems and only to 2D problems; this would all be considered fairly toy-problems by modern SOTA TO research. Compared to foundation models in other science applications (e.g. weather modelling), OAT can't be considered to be a foundation model. And even in this constrained setting it struggles to generalize to OOD cases, as shown in Table 4 (48.55% FR without PP). \n - The failure case (Figure 3, right) looks like OAT has simply memorized it's training dataset and is generating a training datapoint which had loading points close to the test case. Seems likely given the size of OpenTO.\n- Lack of proper reporting of computational costs. [1] suggests that DL methods for TO should provide a clear overview of the entire computational costs of generating the training data, training the model and inference: Only inference costs are measured exactly and a rough time given for training (2 days for the autoencoder, 4 days for the diffusion model without accounting for multiple training runs used for hyperparameter tuning etc.). \n- [1] further suggests DL TO models should provide breakeven estimates, so how many model queries are needed to amortize the dataset generation and training costs. These breakeven calculations are not provided.\n\n[1] WOLDSETH, Rebekka V., et al. On the use of artificial neural networks in topology optimisation. Structural and Multidisciplinary Optimization, 2022, 65. Jg., Nr. 10, S. 294.\n\nQUESTIONS:\n- You don't just consider Dirichlet BC but also Neumann, right? At least in appendix A this should be mentioned at some point for completness.\n- Table 5 reports SIMP runtimes: Are these run on the CPU (single core or multiple cores?) or on the GPU?\n- Can you provide the exact computational cost and break-even points? \n- Failure cases: You report failure cases of OAT (see W2). Do these only appear in OOD test cases? Does OAT consistently fail on these cases or does it produce valid shapes when queried multiple times? Are there (OOD) where OAT fails completely even after multiple queries? \n\nI'm open to discussion and changing my rating if:\n\n- the computational costs/break-evens are included correctly \n- the authors address my points from the Weaknesses section.\n\nOpen question: OAT is a neural surrogate that approximates the entire TO process in a single step from BC to optimized structure. The expensive part in solving many large TO problems are typically not the SIMP updates but the FEM solves. Where do you see the advantages/tradeoffs between the OAT approach and instead developing a FEM neural surrogate to speed up SIMP?\nFor me this seems similar to GANs vs Diffusion/Flow matching, where it has turned out to be much better to transform the noise-to-data distribution in multiple steps instead of in a single stepas in GANs.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 2, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-23"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nTopology optimization is the task of optimizing an engineering design with an evaluation metric that depends on the solution of a PDE, such as the optimization of an airfoil to minimize the drag resulting from the flow field obtained by solving the Navier-Stokes Equations. Such optimization is typically costly and is performed with expensive adjoint-based optimization. In place of this, the paper trains a foundation model for topology optimization for a variety of domain sizes and shapes. In the process, they also develop an extensive dataset of topology optimization tasks and corresponding solutions.\n\nSTRENGTHS AND WEAKNESSES:\nThe primary contribution from this paper is a generally usable dataset of topology optimization tasks. While the component parts of the proposed model are standard, the assembly into a foundation model likely required substantial effort to get functioning, as we elaborate on below.\n\n**Quality**\n\nThe bulk of the work was in considering extensive empirical assessments of the proposed model against other topology optimization approaches. The authors do highlight well the deficiencies in their proposed model, which is more broadly an issue of using black-box machine learning predictors for directly predicting the solutions to such optimization tasks. The assessments are thoroughly conducted against number of different generated benchmark tasks, assessing for the compliance, failure rate, and sampling speed. These three metrics seem quite comprehensive as metrics for assessment and were assessed against some competitor methods.\n\n**Clarity**\n\nThe presentation is well-delivered and writing clear. Figures are also well-illustrated, such as the workflow diagram in Figure 2 and failure diagram in Figure 3. Exposition was easy to follow along throughout the paper.\n\n**Significance**\n\nThe work does contribute significantly in developing a comprehensive suite of topology optimization problems. This alone seems to be a worthwhile contribution, although the additional contribution of the foundational model serves as a good starting point for further exploration in this direction. The pointing out of deficiencies in this direct prediction approach around boundary effects is also a worthwhile contribution. \n\n**Originality**\n\nWhile no individual piece of the pipeline is inherently novel or distinct from their incarnations in previous works, the overall construction of a topology optimization foundation model from these pieces was a novel undertaking as was the generation of plausible topology optimization problems for training the model. More novelty in the foundation model would be interesting to pursue, but this feels like work that would be better suited to further work that builds upon this first step.\n\nQUESTIONS:\n- It seems like data were generated at random in the proposed OpenTO dataset through procedural generation; however, it was not described how this generation is performed. In particular, I would imagine many domain with purely random generation would be implausible, so what are the mechanisms to cull or avoid these domains?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-23"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes OAT (Optimize Any Topology), a resolution-invariant framework that fuses a shared autoencoder, a convolutional local implicit-field renderer, and a conditional latent diffusion model to synthesize near-optimal topology designs for arbitrary aspect ratios, resolutions, volume fractions, loads, and constraints. Leveraging the 2.19 million-example OpenTO dataset covering 2 million distinct boundary conditions, OAT attains sub-1 % compliance error on 64x64 and 256x256 datasets and cuts inference time to faster than SIMP and roughly more accurate than prior neural baselines such as NITO and TopoDiff.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n\n1. **Large, publicly released dataset.** The paper introduces the OpenTO corpus, containing 2.19 M samples and 2 M distinct boundary conditions, which offers the community an unprecedentedly broad and reproducible benchmark for training and evaluating topology-optimization models.\n    \n2. **State-of-the-art accuracy.** On $64\\times 64$–$256\\times 256$ datasets, OAT achieves compliance errors below $1\\%$ without post-optimization, outperforming prior generative baselines such as TopoDiff and NITO by roughly one order of magnitude.\n    \n3. **High versatility.** Thanks to its resolution-invariant latent representation, OAT handles arbitrary aspect ratios, mesh sizes, volume fractions, loads, and boundary constraints without retraining, markedly simplifying deployment across heterogeneous design scenarios.\n    \n\n**Weaknesses**\n\n1. **Attribution of gains to the new dataset is unclear.** OAT is evaluated on OpenTO, whereas competing methods use their original training data; the reported superiority may therefore stem from higher-quality data rather than algorithmic advances. A fair comparison would retrain existing generative approaches on OpenTO (minor architectural adjustments should suffice) to isolate the methodological benefit of OAT itself.\n    \n2. **High failure rate under fully random conditions.** A single forward pass yields $\\approx48$% invalid topologies on the unrestricted OpenTO benchmark, and even after ten SIMP refinement steps the failure rate remains $\\approx16$%, which may limit reliability in safety-critical workflows.\n    \n3. **Dependence on post-optimization.** The recommended 5–10 SIMP iterations needed to “heal” minor deviations contradict the ambition of one-shot optimal generation and diminish real-time performance in high-throughput settings.\n    \n4. **Complex architecture and integration cost.** Combining an autoencoder, an implicit-field renderer, and a conditional diffusion model increases engineering overhead and GPU-memory management complexity compared with single-stage UNet- or NeRF-based generators, potentially impeding adoption in industrial pipelines.\n\nQUESTIONS:\nsee weaknesses.\n\nLIMITATIONS:\nsee weaknesses.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents a foundation framework of structural topology optimization by handling arbitrary boundary conditions, domain shapes, and resolutions. It is a pre-trained latent diffusion model designed for minimum-compliance structural design, marking a foundational advance. In this paper OpenTO Dataset is established including 2.2M samples with arbitrary boundary conditions, shapes, resolutions and forces.  It achieves a 10x reduction in compliance error compared to prior methods. Generates high-resolution topologies maintaining efficiency on the inference.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n1. This topology optimization model can handle arbitrary boundary conditions, resolutions, and aspect ratios, overcoming limitations of prior fixed-grid approaches.\n2. This model achieves very low compliance error without the need for any direct optimization. It is efficient to generates high-resolution topologies with scalable inference.\n3. This paper introduces an OpenTO dataset which contains 2.2 millions structures. The procedural data generation is very clear in Appendix B.\n4. This method could handle mixed shape/resolution data easily.\n\nWeaknesses:\n The computational complexity of the method remains uncharacterized from a mathematical perspective.\n\nQUESTIONS:\n1. E_min in Sections A.1.3 and A.1.4 should provide a more detailed discussion of their interrelationship.\n2. The mathematical symbols used in the vθ formula (line 223) describing the inverse denoising process require clarification. Would you please provide a detailed explanation of this formulation?\n3. In the experimental results, the mean volume fraction error (VFE) was reported. However, another metric VFE (Med) (median volume fraction error), was also used in Reference [31] but not mentioned in this study. Could the authors explain why this metric was not included?\n\nLIMITATIONS:\nyes.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 4, "ORIGINALITY": 4, "DATE": "2025-07-03"}