# 3D Topology Optimization using Convolutional Neural Networks

arXiv: https://arxiv.org/abs/1808.07440 · HTML: https://mlsanity.com/paper/1808.07440/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Aug 2018.

## Built on by (most cited first, 29 of 29)

- [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)
- [Real-Time Topology Optimization in 3D via Deep Transfer Learning](https://mlsanity.com/paper/2102.07657/) (2021)
- [Diffusing the Optimal Topology: A Generative Optimization Approach](https://mlsanity.com/paper/2303.09760/) (2023)
- [Neural topology optimization: the good, the bad, and the ugly](https://mlsanity.com/paper/2407.13954/) (2024)
- [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)
- [Graph Neural Network Based Surrogate Model of Physics Simulations for Geometry Design](https://mlsanity.com/paper/2302.00557/) (2023)
- [Latent Diffusion Models for Structural Component Design](https://mlsanity.com/paper/2309.11601/) (2023)
- [Topology Optimization using Neural Networks with Conditioning Field Initialization for Improved Efficiency](https://mlsanity.com/paper/2305.10460/) (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)
- [Graph Neural Network for Stress Predictions in Stiffened Panels Under Uniform Loading](https://mlsanity.com/paper/2309.13022/) (2023)
- [Trajectory-Aware Flow Matching for Topology Optimisation](https://mlsanity.com/paper/2607.14652/) (2026)
- [A mechanistic-based data-driven approach to accelerate structural topology optimization through finite element convolutional neural network (FE-CNN)](https://mlsanity.com/paper/2106.13652/) (2021)
- [An FEA surrogate model with Boundary Oriented Graph Embedding approach](https://mlsanity.com/paper/2108.13509/) (2021)
- [FRC-TOuNN: Topology Optimization of Continuous Fiber Reinforced Composites using Neural Network](https://mlsanity.com/paper/2205.03737/) (2022)
- [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)
- [Enhanced Data-driven Topology Design Methodology with Multi-level Mesh and Correlation-based Mutation for Stress-related Multi-objective Optimization](https://mlsanity.com/paper/2504.14790/) (2025)
- [SPhyR: Spatial-Physical Reasoning Benchmark on Material Distribution](https://mlsanity.com/paper/2505.16048/) (2025)
- [AutoSiMP: Autonomous Topology Optimization from Natural Language via LLM-Driven Problem Configuration and Adaptive Solver Control](https://mlsanity.com/paper/2603.27000/) (2026)
- [eCNNTO: A Highly Generalizable ConvNet for Accelerating Topology Optimization](https://mlsanity.com/paper/2606.19921/) (2026)
- [How the Classical Baseline Shapes Machine-Learning Speed Claims in Topology Optimization](https://mlsanity.com/paper/2610.16051/) (2026)

## Abstract (arXiv)

Topology optimization is computationally demanding that requires the assembly and solution to a finite element problem for each material distribution hypothesis. As a complementary alternative to the traditional physics-based topology optimization, we explore a data-driven approach that can quickly generate accurate solutions. To this end, we propose a deep learning approach based on a 3D encoder-decoder Convolutional Neural Network architecture for accelerating 3D topology optimization and to determine the optimal computational strategy for its deployment. Analysis of iteration-wise progress of the Solid Isotropic Material with Penalization process is used as a guideline to study how the earlier steps of the conventional topology optimization can be used as input for our approach to predict the final optimized output structure directly from this input. We conduct a comparative study between multiple strategies for training the neural network and assess the effect of using various input combinations for the CNN to finalize the strategy with the highest accuracy in predictions for practical deployment. For the best performing network, we achieved about 40% reduction in overall computation time while also attaining structural accuracies in the order of 96%.