# Neural networks for topology optimization

arXiv: https://arxiv.org/abs/1709.09578 · HTML: https://mlsanity.com/paper/1709.09578/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Sep 2017.

## Built on by (most cited first, 30 of 39)

- [Deep Generative Models in Engineering Design: A Review](https://mlsanity.com/paper/2110.10863/) (2021)
- [Diffusion Models Beat GANs on Topology Optimization](https://mlsanity.com/paper/2208.09591/) (2022)
- [High-Dimensional Bayesian Optimisation with Variational Autoencoders and Deep Metric Learning](https://mlsanity.com/paper/2106.03609/) (2021)
- [Aligning Optimization Trajectories with Diffusion Models for Constrained Design Generation](https://mlsanity.com/paper/2305.18470/) (2023)
- [BIKED: A Dataset for Computational Bicycle Design with Machine Learning Benchmarks](https://mlsanity.com/paper/2103.05844/) (2021)
- [Topology Optimization via Machine Learning and Deep Learning: A Review](https://mlsanity.com/paper/2210.10782/) (2022)
- [Deep Learning in Deterministic Computational Mechanics](https://mlsanity.com/paper/2309.15421/) (2023)
- [Large Language Model Agent as a Mechanical Designer](https://mlsanity.com/paper/2404.17525/) (2024)
- [Modular machine learning-based elastoplasticity: generalization in the context of limited data](https://mlsanity.com/paper/2210.08343/) (2022)
- [Neural topology optimization: the good, the bad, and the ugly](https://mlsanity.com/paper/2407.13954/) (2024)
- [PG-LBO: Enhancing High-Dimensional Bayesian Optimization with Pseudo-Label and Gaussian Process Guidance](https://mlsanity.com/paper/2312.16983/) (2023)
- [Differentiable Visual Computing for Inverse Problems and Machine Learning](https://mlsanity.com/paper/2312.04574/) (2023)
- [EngiBench: A Framework for Data-Driven Engineering Design Research](https://mlsanity.com/paper/2508.00831/) (2025)
- [High-Dimensional Bayesian Optimization via Semi-Supervised Learning with Optimized Unlabeled Data Sampling](https://mlsanity.com/paper/2305.02614/) (2023)
- [Latent Diffusion Models for Structural Component Design](https://mlsanity.com/paper/2309.11601/) (2023)
- [On the Generalization in Topology Optimization via Sensitivity-Conditioned Bernoulli Flow Matching](https://mlsanity.com/paper/2606.02179/) (2026)
- [iPINNs: Incremental learning for Physics-informed neural networks](https://mlsanity.com/paper/2304.04854/) (2023)
- [NITO: Neural Implicit Fields for Resolution-free Topology Optimization](https://mlsanity.com/paper/2402.05073/) (2024)
- [Speeding up Computational Morphogenesis with Online Neural Synthetic Gradients](https://mlsanity.com/paper/2104.12282/) (2021)
- [GANTL: Towards Practical and Real-Time Topology Optimization with Conditional GANs and Transfer Learning](https://mlsanity.com/paper/2105.03045/) (2021)
- [DNN-Based Topology Optimisation: Spatial Invariance and Neural Tangent Kernel](https://mlsanity.com/paper/2106.05710/) (2021)
- [Robust Topology Optimization Using Multi-Fidelity Variational Autoencoders](https://mlsanity.com/paper/2107.10661/) (2021)
- [Gradient-free neural topology optimization: Towards effective fracture-resistant designs](https://mlsanity.com/paper/2403.04937/) (2024)
- [Inverse design with conditional cascaded diffusion models](https://mlsanity.com/paper/2408.08526/) (2024)
- [An Adaptive and Scalable ANN-based Model-Order-Reduction Method for Large-Scale TO Designs](https://mlsanity.com/paper/2203.10515/) (2022)
- [Diverse Topology Optimization using Modulated Neural Fields](https://mlsanity.com/paper/2502.13174/) (2025)
- [Large Language Models as Optimization Controllers: Adaptive Continuation for SIMP Topology Optimization](https://mlsanity.com/paper/2603.25099/) (2026)
- [Trajectory-Aware Flow Matching for Topology Optimisation](https://mlsanity.com/paper/2607.14652/) (2026)
- [Adversarial Agents on Topology Optimization: Understanding the Fragility and Robustness of Deep Learning-based and Physics-Based Design Models under Adversarial Perturbation](https://mlsanity.com/paper/2608.22606/) (2026)
- [HGTO: A Unified Graph-Based Physics-Informed Formulation for Structural Topology Optimization](https://mlsanity.com/paper/2609.15001/) (2026)

## Abstract (arXiv)

In this research, we propose a deep learning based approach for speeding up the topology optimization methods. The problem we seek to solve is the layout problem. The main novelty of this work is to state the problem as an image segmentation task. We leverage the power of deep learning methods as the efficient pixel-wise image labeling technique to perform the topology optimization. We introduce convolutional encoder-decoder architecture and the overall approach of solving the above-described problem with high performance. The conducted experiments demonstrate the significant acceleration of the optimization process. The proposed approach has excellent generalization properties. We demonstrate the ability of the application of the proposed model to other problems. The successful results, as well as the drawbacks of the current method, are discussed.