# A deep Convolutional Neural Network for topology optimization with strong generalization ability

arXiv: https://arxiv.org/abs/1901.07761 · HTML: https://mlsanity.com/paper/1901.07761/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2019.

## Built on by (most cited first, 17 of 17)

- [NTopo: Mesh-free Topology Optimization using Implicit Neural Representations](https://mlsanity.com/paper/2102.10782/) (2021)
- [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)
- [Real-Time Topology Optimization in 3D via Deep Transfer Learning](https://mlsanity.com/paper/2102.07657/) (2021)
- [De-homogenization using Convolutional Neural Networks](https://mlsanity.com/paper/2105.04232/) (2021)
- [An adaptive artificial neural network-based generative design method for layout designs](https://mlsanity.com/paper/2101.12410/) (2021)
- [Latent Diffusion Models for Structural Component Design](https://mlsanity.com/paper/2309.11601/) (2023)
- [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)
- [Exploring the structure-property relations of thin-walled, 2D extruded lattices using neural networks](https://mlsanity.com/paper/2205.06761/) (2022)
- [An FEA surrogate model with Boundary Oriented Graph Embedding approach](https://mlsanity.com/paper/2108.13509/) (2021)
- [SELTO: Sample-Efficient Learned Topology Optimization](https://mlsanity.com/paper/2209.05098/) (2022)
- [Data-driven topology design based on principal component analysis for 3D structural design problems](https://mlsanity.com/paper/2409.01607/) (2024)
- [ExIQA: Explainable Image Quality Assessment Using Distortion Attributes](https://mlsanity.com/paper/2409.06853/) (2024)
- [SPhyR: Spatial-Physical Reasoning Benchmark on Material Distribution](https://mlsanity.com/paper/2505.16048/) (2025)
- [How the Classical Baseline Shapes Machine-Learning Speed Claims in Topology Optimization](https://mlsanity.com/paper/2610.16051/) (2026)

## Abstract (arXiv)

This paper proposes a deep Convolutional Neural Network(CNN) with strong generalization ability for structural topology optimization. The architecture of the neural network is made up of encoding and decoding parts, which provide down- and up-sampling operations. In addition, a popular technique, namely U-Net, was adopted to improve the performance of the proposed neural network. The input of the neural network is a well-designed tensor with each channel includes different information for the problem, and the output is the layout of the optimal structure. To train the neural network, a large dataset is generated by a conventional topology optimization approach, i.e. SIMP. The performance of the proposed method was evaluated by comparing its efficiency and accuracy with SIMP on a series of typical optimization problems. Results show that a significant reduction in computation cost was achieved with little sacrifice on the optimality of design solutions. Furthermore, the proposed method can intelligently solve problems under boundary conditions not being included in the training dataset.