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

arXiv 2003.04685 ↗First posted 5 Mar 2020cs.CE cs.AI eess.IVcited by 65

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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.

Key facts. Cited by 65 papers in the map (data through 7 Oct 2026). First posted on arXiv 5 Mar 2020.

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Citing papers per year: 2021: 10; 2022: 8; 2023: 16; 2024: 10; 2025: 4; 2026: 17.

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  1. 2021Deep Generative Models in Engineering Design: A Reviewcited by 103
  2. 2024Physics-Informed Diffusion Modelscited by 88
  3. 2022Diffusion Models Beat GANs on Topology Optimizationcited by 79
  4. 2023Aligning Optimization Trajectories with Diffusion Models for Constrained Design Generationcited by 51
  5. 2023From Concept to Manufacturing: Evaluating Vision-Language Models for Engineering Designcited by 51
  6. 2021NTopo: Mesh-free Topology Optimization using Implicit Neural Representationscited by 41
  7. 2022Topology Optimization via Machine Learning and Deep Learning: A Reviewcited by 22
  8. 2023Beyond Statistical Similarity: Rethinking Metrics for Deep Generative Models in Engineering Designcited by 22
  9. 2022Generative Transformers for Design Concept Generationcited by 21
  10. 2023Deep Learning in Deterministic Computational Mechanicscited by 21
  11. 2024Large Language Model Agent as a Mechanical Designercited by 20
  12. 2021Activation Landscapes as a Topological Summary of Neural Network Performancecited by 17
38 more
  1. 2021Generative Pre-Trained Transformer for Design Concept Generation: An Explorationcited by 17
  2. 2023Recent Advances and Applications of Machine Learning in Experimental Solid Mechanics: A Reviewcited by 15
  3. 2022FRAMED: An AutoML Approach for Structural Performance Prediction of Bicycle Framescited by 11
  4. 2023Constraining Generative Models for Engineering Design with Negative Datacited by 11
  5. 2023ShipHullGAN: A generic parametric modeller for ship hull design using deep convolutional generative modelcited by 10
  6. 2023Diffusing the Optimal Topology: A Generative Optimization Approachcited by 9
  7. 2021Airfoil GAN: Encoding and Synthesizing Airfoils for Aerodynamic Shape Optimizationcited by 7
  8. 2021De-homogenization using Convolutional Neural Networkscited by 6
  9. 2023DMF-TONN: Direct Mesh-free Topology Optimization using Neural Networkscited by 6
  10. 2022Concurrent build direction, part segmentation, and topology optimization for additive manufacturing using neural networkscited by 5
  11. 2023DADO -- Low-Cost Query Strategies for Deep Active Design Optimizationcited by 4
  12. 2023Latent Diffusion Models for Structural Component Designcited by 4
  13. 2026On the Generalization in Topology Optimization via Sensitivity-Conditioned Bernoulli Flow Matchingcited by 4
  14. 2023Topology Optimization using Neural Networks with Conditioning Field Initialization for Improved Efficiencycited by 3
  15. 2023Dynamically configured physics-informed neural network in topology optimization applicationscited by 3
  16. 2024NITO: Neural Implicit Fields for Resolution-free Topology Optimizationcited by 3
  17. 2026GIFT: Bootstrapping Image-to-CAD Program Synthesis via Geometric Feedbackcited by 3
  18. 2026EngiAI: Capability-Based Evaluation of Tool-Connected LLM Agents for Engineering Designcited by 3
  19. 2021DNN-Based Topology Optimisation: Spatial Invariance and Neural Tangent Kernelcited by 2
  20. 2024Gradient-free neural topology optimization: Towards effective fracture-resistant designscited by 2
  21. 2024Deep Generative Design for Mass Productioncited by 2
  22. 2024Inverse design with conditional cascaded diffusion modelscited by 2
  23. 2025Compliance Minimization via Physics-Informed Gaussian Processescited by 2
  24. 2025Optimize Any Topology: A Foundation Model for Shape- and Resolution-Free Structural Topology Optimizationcited by 2
  25. 2021GANTL: Towards Practical and Real-Time Topology Optimization with Conditional GANs and Transfer Learningcited by 1
  26. 2022Image-based Artificial Intelligence empowered surrogate model and shape morpher for real-time blank shape optimisation in the hot stamping processcited by 1
  27. 2023Graph Neural Network for Stress Predictions in Stiffened Panels Under Uniform Loadingcited by 1
  28. 2024Deep Generative Model-based Synthesis of Four-bar Linkage Mechanisms with Target Conditionscited by 1
  29. 2024Multi-scale Topology Optimization using Neural Networkscited by 1
  30. 2026Multi-material Multi-physics Topology Optimization with Physics-informed Gaussian Process Priorscited by 1
  31. 2026Large Language Models as Optimization Controllers: Adaptive Continuation for SIMP Topology Optimizationcited by 1
  32. 2026HPG-Diff: Hierarchical physics-guided diffusion with differentiable connectivity constraints for topology optimizationcited by 1
  33. 2026Trajectory-Aware Flow Matching for Topology Optimisationcited by 1
  34. 2021SuperMeshing: A New Deep Learning Architecture for Increasing the Mesh Density of Metal Forming Stress Field with Attention Mechanism and Perceptual Featurescited by 0
  35. 2021An FEA surrogate model with Boundary Oriented Graph Embedding approachcited by 0
  36. 2022FRC-TOuNN: Topology Optimization of Continuous Fiber Reinforced Composites using Neural Networkcited by 0
  37. 2022SELTO: Sample-Efficient Learned Topology Optimizationcited by 0
  38. 2023Data-driven intelligent computational design for products: Method, techniques, and applicationscited by 0

50 most cited of 65 All 65 (JSON)