# Deep learning for determining a near-optimal topological design without any iteration

arXiv: https://arxiv.org/abs/1801.05463 · HTML: https://mlsanity.com/paper/1801.05463/

## Key facts

- Cited by 40 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jan 2018.

## Built on by (most cited first, 30 of 40)

- [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)
- [Aligning Optimization Trajectories with Diffusion Models for Constrained Design Generation](https://mlsanity.com/paper/2305.18470/) (2023)
- [NTopo: Mesh-free Topology Optimization using Implicit Neural Representations](https://mlsanity.com/paper/2102.10782/) (2021)
- [Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing](https://mlsanity.com/paper/2211.07377/) (2022)
- [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)
- [Real-Time Topology Optimization in 3D via Deep Transfer Learning](https://mlsanity.com/paper/2102.07657/) (2021)
- [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)
- [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)
- [Latent Diffusion Models for Structural Component Design](https://mlsanity.com/paper/2309.11601/) (2023)
- [Neural Networks for Generating Better Local Optima in Topology Optimization](https://mlsanity.com/paper/2407.17957/) (2024)
- [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)
- [A surrogate model for topology optimisation of elastic structures via parametric autoencoders](https://mlsanity.com/paper/2507.22539/) (2025)
- [Optimize Any Topology: A Foundation Model for Shape- and Resolution-Free Structural Topology Optimization](https://mlsanity.com/paper/2510.23667/) (2025)
- [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)
- [Robust Topology Optimization Using Multi-Fidelity Variational Autoencoders](https://mlsanity.com/paper/2107.10661/) (2021)
- [Conditional Generative Models for Simulation of EMG During Naturalistic Movements](https://mlsanity.com/paper/2211.01856/) (2022)
- [Deep Generative Design for Mass Production](https://mlsanity.com/paper/2403.12098/) (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)
- [Deep Generative Model-based Synthesis of Four-bar Linkage Mechanisms with Target Conditions](https://mlsanity.com/paper/2402.14882/) (2024)
- [A generative adversarial network optimization method for damage detection and digital twinning by deep AI fault learning: Z24 Bridge structural health monitoring benchmark validation](https://mlsanity.com/paper/2511.00099/) (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)

## Abstract (arXiv)

In this study, we propose a novel deep learning-based method to predict an optimized structure for a given boundary condition and optimization setting without using any iterative scheme. For this purpose, first, using open-source topology optimization code, datasets of the optimized structures paired with the corresponding information on boundary conditions and optimization settings are generated at low (32 x 32) and high (128 x 128) resolutions. To construct the artificial neural network for the proposed method, a convolutional neural network (CNN)-based encoder and decoder network is trained using the training dataset generated at low resolution. Then, as a two-stage refinement, the conditional generative adversarial network (cGAN) is trained with the optimized structures paired at both low and high resolutions, and is connected to the trained CNN-based encoder and decoder network. The performance evaluation results of the integrated network demonstrate that the proposed method can determine a near-optimal structure in terms of pixel values and compliance with negligible computational time.