Abstract
In this paper, a simple deep learning network (DLN) based on the geometry parameters of moving morphable bars (MMBs) was proposed for the data-driven optimal topology prediction. The MMBs-based topology optimization approach is adopted to generate datasets that contain optimized topologies described by the geometry parameters. The DLN is simply built based on linear regression using a rectified linear unit (ReLU) activation function to minimize the loss function, which can be measured by the mean square error of the geometry parameters. The proposed approach could instantaneously provide an appropriate topology optimization design once the DLN has been trained. This approach does not require finite element analysis, design variable update, and other computations (e.g., sensitivity analysis) as often seen in the existing topology optimization approaches. Compared to the DLN based on element densities, the number of design variables and training time can be reduced significantly; the gray elements in void zones can also be also discarded.
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Acknowledgements
Research is supported by Vingroup Innovation Foundation (VINIF) in project code VINIF.2019.DA04 and the Alexander von Humboldt Foundation for a Digital Cooperation Fellowship.
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Appendix
Appendix
1.1 A1: Dependence of the loss function and the mean square error on the number of hidden layer nodes (3 hidden layers, the batch size is 128)
Number of nodes in each hidden layer | ||||
|---|---|---|---|---|
500 | 1000 | 1500 | 2000 | |
Loss | 0.0055 | 0.0035 | 0.0026 | 0.0024 |
MSE | 0.0435 | 0.0364 | 0.0316 | 0.0300 |
1.2 A2: Dependence of the loss function and the mean square error on the number of hidden layers (2000 nodes for each hidden layer, the batch size is 128)
Number of hidden layers | ||||
|---|---|---|---|---|
2 | 3 | 4 | 5 | |
Loss | 0.0037 | 0.0024 | 0.0022 | 0.0033 |
MSE | 0.0385 | 0.0300 | 0.0287 | 0.0383 |
1.3 A3: Dependence of the loss function and the mean square error on the batch size (3 hidden layers, 2000 nodes for each hidden layer)
Batch size | ||||
|---|---|---|---|---|
32 | 64 | 128 | 256 | |
Loss | 0.0022 | 0.0021 | 0.0024 | 0.0035 |
MSE | 0.0285 | 0.0277 | 0.0300 | 0.0382 |
1.4 A4: Dependence of the loss function and the mean square error on the number of training data points (3 hidden layers, 2000 nodes for each hidden layer, the batch size is 128)
Number of training data points | ||||
|---|---|---|---|---|
749 (20% dataset) | 1498 (40% dataset) | 2246 (60% dataset) | 2995 (80% dataset) | |
Loss | 0.0071 | 0.0047 | 0.0030 | 0.0024 |
MSE | 0.0589 | 0.0462 | 0.0356 | 0.0300 |
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Hoang, VN., Nguyen, NL., Tran, D.Q. et al. Data-driven geometry-based topology optimization. Struct Multidisc Optim 65, 69 (2022). https://doi.org/10.1007/s00158-022-03170-8
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DOI: https://doi.org/10.1007/s00158-022-03170-8