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Real-time topology optimization based on convolutional neural network by using retrain skill

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Abstract

To realize a real-time structural topology optimization (TO), it is essential to use the information during the TO process. A step-to-step training method is proposed to improve the deep learning model prediction accuracy based on the solid isotropic material with penalization (SIMP) TO method. By increasing the use of optimization history information (such as the structure density matrix), the step-to-step method improves the model utilization efficiency for each sample data. This training method can effectively improve the deep learning model prediction accuracy without increasing the sample set size. The step-to-step training method combines several independent deep learning models (sub-models). The sub-models could have the same model layers and hyperparameters. It can be trained in parallel to speed up the training process. During the deep learning model training process, these features reduce the difficulties in adjusting sub-model parameters and the model training time cost. Meanwhile, this method is achieved by the local end-to-end training process. During the deep learning model predicting process, the increase in total prediction time cost can be ignored. The trained deep learning models can predict the optimized structures in real time. Maximization of first eigenfrequency topology optimization problem with three constraint conditions is used to verify the effectiveness of the proposed training method. The method proposed in this study provides an implementation technology for the real-time TO of structures. The authors also provide the deep learning model code and the dataset in this manuscript (git-hub).

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Data availability

The data set and deep learning model code are available from the “https://github.com/893801366/Real-time-topology-optimization-based-on-convolutional-neural-network-by-using-retrain-skill.git” (git-hub).

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Funding

This research was financially supported by the National Natural Science Foundation of China (No. U1906233,11732004), the Key R&D Program of Shandong Province (2019JZZY010801), the Fundamental Research Funds for the Central Universities (DUT20ZD213, DUT20LAB308).

Author information

Authors and Affiliations

  1. Department of Engineering Mechanics, Dalian University of Technology, No. 2 Linggong Road, Ganjingzi District, Dalian, 116024, Liaoning Province, China

    Jun Yan, Dongling Geng & Qi Xu

  2. School of Engineering, Cardiff University, S2.10C, Queen’s Buildings, South Building, 5 The Parade, Newport Road, Cardiff, CF24 3AA, UK

    Haijiang Li

Authors
  1. Jun Yan
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  2. Dongling Geng
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  3. Qi Xu
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Contributions

All authors contributed to the study conception and design. All authors commented on previous versions of the manuscript. All authors read and approved the final manuscript. JY: conceptualization, project administration, reviewing and editing. DG: discussion with jun yan for the conceptualization, data collection, material preparation, programming, writing-original draft, writing-review & editing. QX: discussion, reviewing and editing. HL: discussion, reviewing and editing.

Corresponding authors

Correspondence to Jun Yan or Haijiang Li.

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Appendix: The total trainable parameters in the model

Appendix: The total trainable parameters in the model

This table shows the feature map size and trainable parameters in each layer. The change of feature map size reflects the operation time of up-sampling and down-sampling in the two models. The trainable parameters refer to the weight and bias parameters of neurons in each layer (such as the convolution layer or down/up sampling layer). These parameters will change during the model training process. Therefore, the trainable parameter size will affect the model training efficiency. The layers without trainable parameters are omitted (such as the dropout layer or add layer).

The model with reducing part

The model without reducing part

Feature map size

Parameters

Feature map size

Parameters

(221, 31, 1)

0

(221, 31, 1)

0

(221, 31, 8)

80

(221, 31, 8)

80

(220, 30, 32)

1056

(220, 30, 32)

1056

(220, 30, 32)

9248

(220, 30, 32)

9248

(110, 15, 64)

8256

(110, 15, 64)

8256

(110, 15, 64)

36,928

(110, 15, 64)

36,928

(55, 14, 128)

32,896

(55, 14, 128)

32,896

(55, 14, 128)

147,584

(55, 14, 128)

147,584

(27, 7, 256)

196,864

(27, 7, 256)

196,864

(27, 7, 256)

590,080

(27, 7, 256)

590,080

(13, 6, 512)

786,944

(13, 6, 512)

786,944

(27, 7, 256)

786,688

(27, 7, 256)

786,688

(27, 7, 256)

590,080

(27, 7, 256)

590,080

(55, 14, 128)

196,736

(55, 14, 128)

196,736

(55, 14, 128)

147,584

(55, 14, 128)

147,584

(110, 15, 64)

32,832

(110, 15, 64)

32,832

(110, 15, 64)

36,928

(110, 15, 64)

36,928

(220, 30, 32)

8224

(220, 30, 32)

8,224

(220, 30, 32)

9248

(220, 30, 32)

9,248

(221, 31, 16)

2064

(221, 31, 16)

2,064

(221, 31, 16)

2320

(221, 31, 16)

2,320

(221, 31, 8)

1160

(221, 31, 8)

1,160

(221, 31, 4)

292

(221, 31, 4)

292

(221, 31, 1)

337

(6851, 1)

187,751,655

Total Parameters

3,624,129

Total Parameters

191,375,747

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Yan, J., Geng, D., Xu, Q. et al. Real-time topology optimization based on convolutional neural network by using retrain skill. Engineering with Computers 39, 4045–4059 (2023). https://doi.org/10.1007/s00366-023-01846-3

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