# TopologyGAN: Topology Optimization Using Generative Adversarial Networks Based on Physical Fields Over the Initial Domain

arXiv: https://arxiv.org/abs/2003.04685 · HTML: https://mlsanity.com/paper/2003.04685/

## Key facts

- Cited by 65 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Mar 2020.

## Built on by (most cited first, 30 of 65)

- [Deep Generative Models in Engineering Design: A Review](https://mlsanity.com/paper/2110.10863/) (2021)
- [Physics-Informed Diffusion Models](https://mlsanity.com/paper/2403.14404/) (2024)
- [Diffusion Models Beat GANs on Topology Optimization](https://mlsanity.com/paper/2208.09591/) (2022)
- [Aligning Optimization Trajectories with Diffusion Models for Constrained Design Generation](https://mlsanity.com/paper/2305.18470/) (2023)
- [From Concept to Manufacturing: Evaluating Vision-Language Models for Engineering Design](https://mlsanity.com/paper/2311.12668/) (2023)
- [NTopo: Mesh-free Topology Optimization using Implicit Neural Representations](https://mlsanity.com/paper/2102.10782/) (2021)
- [Topology Optimization via Machine Learning and Deep Learning: A Review](https://mlsanity.com/paper/2210.10782/) (2022)
- [Beyond Statistical Similarity: Rethinking Metrics for Deep Generative Models in Engineering Design](https://mlsanity.com/paper/2302.02913/) (2023)
- [Generative Transformers for Design Concept Generation](https://mlsanity.com/paper/2211.03468/) (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)
- [Activation Landscapes as a Topological Summary of Neural Network Performance](https://mlsanity.com/paper/2110.10136/) (2021)
- [Generative Pre-Trained Transformer for Design Concept Generation: An Exploration](https://mlsanity.com/paper/2111.08489/) (2021)
- [Recent Advances and Applications of Machine Learning in Experimental Solid Mechanics: A Review](https://mlsanity.com/paper/2303.07647/) (2023)
- [FRAMED: An AutoML Approach for Structural Performance Prediction of Bicycle Frames](https://mlsanity.com/paper/2201.10459/) (2022)
- [ShipHullGAN: A generic parametric modeller for ship hull design using deep convolutional generative model](https://mlsanity.com/paper/2305.00210/) (2023)
- [Constraining Generative Models for Engineering Design with Negative Data](https://mlsanity.com/paper/2306.15166/) (2023)
- [Diffusing the Optimal Topology: A Generative Optimization Approach](https://mlsanity.com/paper/2303.09760/) (2023)
- [Airfoil GAN: Encoding and Synthesizing Airfoils for Aerodynamic Shape Optimization](https://mlsanity.com/paper/2101.04757/) (2021)
- [De-homogenization using Convolutional Neural Networks](https://mlsanity.com/paper/2105.04232/) (2021)
- [DMF-TONN: Direct Mesh-free Topology Optimization using Neural Networks](https://mlsanity.com/paper/2305.04107/) (2023)
- [Concurrent build direction, part segmentation, and topology optimization for additive manufacturing using neural networks](https://mlsanity.com/paper/2210.01315/) (2022)
- [Latent Diffusion Models for Structural Component Design](https://mlsanity.com/paper/2309.11601/) (2023)
- [DADO -- Low-Cost Query Strategies for Deep Active Design Optimization](https://mlsanity.com/paper/2307.04536/) (2023)
- [On the Generalization in Topology Optimization via Sensitivity-Conditioned Bernoulli Flow Matching](https://mlsanity.com/paper/2606.02179/) (2026)
- [Topology Optimization using Neural Networks with Conditioning Field Initialization for Improved Efficiency](https://mlsanity.com/paper/2305.10460/) (2023)
- [Dynamically configured physics-informed neural network in topology optimization applications](https://mlsanity.com/paper/2312.06993/) (2023)
- [NITO: Neural Implicit Fields for Resolution-free Topology Optimization](https://mlsanity.com/paper/2402.05073/) (2024)
- [Optimize Any Topology: A Foundation Model for Shape- and Resolution-Free Structural Topology Optimization](https://mlsanity.com/paper/2510.23667/) (2025)
- [GIFT: Bootstrapping Image-to-CAD Program Synthesis via Geometric Feedback](https://mlsanity.com/paper/2603.27448/) (2026)

## Abstract (arXiv)

In topology optimization using deep learning, load and boundary conditions represented as vectors or sparse matrices often miss the opportunity to encode a rich view of the design problem, leading to less than ideal generalization results. We propose a new data-driven topology optimization model called TopologyGAN that takes advantage of various physical fields computed on the original, unoptimized material domain, as inputs to the generator of a conditional generative adversarial network (cGAN). Compared to a baseline cGAN, TopologyGAN achieves a nearly 3× reduction in the mean squared error and a 2.5× reduction in the mean absolute error on test problems involving previously unseen boundary conditions. Built on several existing network models, we also introduce a hybrid network called U-SE(Squeeze-and-Excitation)-ResNet for the generator that further increases the overall accuracy. We publicly share our full implementation and trained network.