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An Improved Data-Driven Topology Optimization Method Using Feature Pyramid Networks with Physical Constraints

Jiaxiang Luo1,2, Yu Li2, Weien Zhou2, Zhiqiang Gong2, Zeyu Zhang1, Wen Yao2,*

1 College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, 410073, China
2 National Innovation Institute of Defense Technology, Chinese Academy of Military Science, Beijing, 100000, China

* Corresponding Author: Wen Yao. Email:

(This article belongs to this Special Issue: Novel Methods of Topology Optimization and Engineering Applications)

Computer Modeling in Engineering & Sciences 2021, 128(3), 823-848.


Deep learning for topology optimization has been extensively studied to reduce the cost of calculation in recent years. However, the loss function of the above method is mainly based on pixel-wise errors from the image perspective, which cannot embed the physical knowledge of topology optimization. Therefore, this paper presents an improved deep learning model to alleviate the above difficulty effectively. The feature pyramid network (FPN), a kind of deep learning model, is trained to learn the inherent physical law of topology optimization itself, of which the loss function is composed of pixel-wise errors and physical constraints. Since the calculation of physical constraints requires finite element analysis (FEA) with high calculating costs, the strategy of adjusting the time when physical constraints are added is proposed to achieve the balance between the training cost and the training effect. Then, two classical topology optimization problems are investigated to verify the effectiveness of the proposed method. The results show that the developed model using a small number of samples can quickly obtain the optimization structure without any iteration, which has not only high pixel-wise accuracy but also good physical performance.


Cite This Article

Luo, J., Li, Y., Zhou, W., Gong, Z., Zhang, Z. et al. (2021). An Improved Data-Driven Topology Optimization Method Using Feature Pyramid Networks with Physical Constraints. CMES-Computer Modeling in Engineering & Sciences, 128(3), 823–848.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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