# How the Classical Baseline Shapes Machine-Learning Speed Claims in Topology Optimization

arXiv: https://arxiv.org/abs/2610.16051 · HTML: https://mlsanity.com/paper/2610.16051/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 38 of its 95 references that are in the map.
- First posted on arXiv 12 Oct 2026.

## Builds on (most cited first, 30 of 38)

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- [Deep Generative Models in Engineering Design: A Review](https://mlsanity.com/paper/2110.10863/) (2021)
- [Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations](https://mlsanity.com/paper/2407.07218/) (2024)
- [Deep Generative Modeling for Mechanistic-based Learning and Design of Metamaterial Systems](https://mlsanity.com/paper/2006.15274/) (2020)
- [On the use of Artificial Neural Networks in Topology Optimisation](https://mlsanity.com/paper/2208.02563/) (2022)
- [3D Topology Optimization using Convolutional Neural Networks](https://mlsanity.com/paper/1808.07440/) (2018)
- [Data-driven topology optimization of spinodoid metamaterials with seamlessly tunable anisotropy](https://mlsanity.com/paper/2012.15744/) (2020)
- [Topology Optimization via Machine Learning and Deep Learning: A Review](https://mlsanity.com/paper/2210.10782/) (2022)
- [A Novel Topology Optimization Approach using Conditional Deep Learning](https://mlsanity.com/paper/1901.04859/) (2019)
- [A deep Convolutional Neural Network for topology optimization with strong generalization ability](https://mlsanity.com/paper/1901.07761/) (2019)
- [A Parametric Level Set Method for Topology Optimization based on Deep Neural Network (DNN)](https://mlsanity.com/paper/2101.03286/) (2021)
- [Length Scale Control in Topology Optimization using Fourier Enhanced Neural Networks](https://mlsanity.com/paper/2109.01861/) (2021)
- [Diffusing the Optimal Topology: A Generative Optimization Approach](https://mlsanity.com/paper/2303.09760/) (2023)
- [Neural topology optimization: the good, the bad, and the ugly](https://mlsanity.com/paper/2407.13954/) (2024)
- [De-homogenization using Convolutional Neural Networks](https://mlsanity.com/paper/2105.04232/) (2021)
- [Latent Diffusion Models for Structural Component Design](https://mlsanity.com/paper/2309.11601/) (2023)
- [Neural Level Set Topology Optimization Using Unfitted Finite Elements](https://mlsanity.com/paper/2303.13672/) (2023)
- [Topology Optimization with Text-Guided Stylization](https://mlsanity.com/paper/2310.15506/) (2023)
- [Neural Networks for Generating Better Local Optima in Topology Optimization](https://mlsanity.com/paper/2407.17957/) (2024)
- [Deep learning-based topological optimization for representing a user-specified design area](https://mlsanity.com/paper/2004.05461/) (2020)
- [Optimize Any Topology: A Foundation Model for Shape- and Resolution-Free Structural Topology Optimization](https://mlsanity.com/paper/2510.23667/) (2025)
- [GANTL: Towards Practical and Real-Time Topology Optimization with Conditional GANs and Transfer Learning](https://mlsanity.com/paper/2105.03045/) (2021)
- [Robust Topology Optimization Using Multi-Fidelity Variational Autoencoders](https://mlsanity.com/paper/2107.10661/) (2021)
- [Multi-material Multi-physics Topology Optimization with Physics-informed Gaussian Process Priors](https://mlsanity.com/paper/2602.17783/) (2026)
- [Partial Differential Equations in the Age of Machine Learning: A Critical Synthesis of Classical, Machine Learning, and Hybrid Methods](https://mlsanity.com/paper/2603.07655/) (2026)

## Abstract (arXiv)

Topology optimization places material so that a structure resists deformation under given loads. Machine-learning methods often report large speed-ups over classical, non-learned optimization, but a slow classical code or a less stiff learned design can exaggerate them. We re-ran released code for eight methods on one workstation and studied two in depth: Optimize Any Topology (OAT), a diffusion model that generates designs, and a graph-based neural optimizer. Speeding up only the classical code's finite-element solver cut these two methods' speed-ups by up to 20-fold. We then timed the classical code until its design was at least as stiff as the learned one; for OAT, we read this point off the completed runs. Published timings imply a 134x speed-up for OAT on a 256 x 256 grid; our matched single-design comparisons gave 1.5x to 3.5x. At matched stiffness, the graph-based optimizer was slower than the classical code in all six two-dimensional problems. Of the six other methods, two kept their advantage, one shrank, one reversed and two were not comparable. In an exploratory audit of published claims, language models judged that 8 of 28 speed comparisons in randomly sampled, openly accessible articles lacked evidence of equal design quality; our own review counted 11, so the count depends on who judges. We provide a comparison procedure and a minimum report: classical code, hardware, design quality, what each timing includes, and data-generation and training costs.