# Real-Time Topology Optimization in 3D via Deep Transfer Learning

arXiv: https://arxiv.org/abs/2102.07657 · HTML: https://mlsanity.com/paper/2102.07657/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 44 references that are in the map.
- First posted on arXiv 11 Feb 2021.

## Builds on (most cited first, 6 of 6)

- [A Review of Convolutional Neural Networks for Inverse Problems in Imaging](https://mlsanity.com/paper/1710.04011/) (2017)
- [Deep learning for determining a near-optimal topological design without any iteration](https://mlsanity.com/paper/1801.05463/) (2018)
- [3D Topology Optimization using Convolutional Neural Networks](https://mlsanity.com/paper/1808.07440/) (2018)
- [A Novel Topology Optimization Approach using Conditional Deep Learning](https://mlsanity.com/paper/1901.04859/) (2019)
- [A deep Convolutional Neural Network for topology optimization with strong generalization ability](https://mlsanity.com/paper/1901.07761/) (2019)
- [A New CGAN Technique for Constrained Topology Design Optimization](https://mlsanity.com/paper/1901.07675/) (2019)

## Built on by (most cited first, 14 of 14)

- [Deep Generative Models in Engineering Design: A Review](https://mlsanity.com/paper/2110.10863/) (2021)
- [Aligning Optimization Trajectories with Diffusion Models for Constrained Design Generation](https://mlsanity.com/paper/2305.18470/) (2023)
- [Large Language Model Agent as a Mechanical Designer](https://mlsanity.com/paper/2404.17525/) (2024)
- [Diffusing the Optimal Topology: A Generative Optimization Approach](https://mlsanity.com/paper/2303.09760/) (2023)
- [Weakly-Supervised Deep Learning Model for Prostate Cancer Diagnosis and Gleason Grading of Histopathology Images](https://mlsanity.com/paper/2212.12844/) (2022)
- [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)
- [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)
- [NITO: Neural Implicit Fields for Resolution-free Topology Optimization](https://mlsanity.com/paper/2402.05073/) (2024)
- [GANTL: Towards Practical and Real-Time Topology Optimization with Conditional GANs and Transfer Learning](https://mlsanity.com/paper/2105.03045/) (2021)
- [Inverse design with conditional cascaded diffusion models](https://mlsanity.com/paper/2408.08526/) (2024)
- [Trajectory-Aware Flow Matching for Topology Optimisation](https://mlsanity.com/paper/2607.14652/) (2026)
- [Machine learning for structural design models of continuous beam systems via influence zones](https://mlsanity.com/paper/2403.09454/) (2024)

## Abstract (arXiv)

The published literature on topology optimization has exploded over the last two decades to include methods that use shape and topological derivatives or evolutionary algorithms formulated on various geometric representations and parametrizations. One of the key challenges of all these methods is the massive computational cost associated with 3D topology optimization problems. We introduce a transfer learning method based on a convolutional neural network that (1) can handle high-resolution 3D design domains of various shapes and topologies; (2) supports real-time design space explorations as the domain and boundary conditions change; (3) requires a much smaller set of high-resolution examples for the improvement of learning in a new task compared to traditional deep learning networks; (4) is multiple orders of magnitude more efficient than the established gradient-based methods, such as SIMP. We provide numerous 2D and 3D examples to showcase the effectiveness and accuracy of our proposed approach, including for design domains that are unseen to our source network, as well as the generalization capabilities of the transfer learning-based approach. Our experiments achieved an average binary accuracy of around 95% at real-time prediction rates. These properties, in turn, suggest that the proposed transfer-learning method may serve as the first practical underlying framework for real-time 3D design exploration based on topology optimization