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The rapid development of deep learning has brought new opportunities for the exploration of topology optimization methods. The combination of deep learning and topology optimization has become one of the hottest research fields at the moment. In this work, the neural network is directly used for topology optimization. The update of the design variables (pseudo-density) in the conventional topology optimization method is transformed into the update of the neural network's parameters, which is called **_Neural Reparameterization_**. The sensitivity analysis in the conventional topology optimization method is realized by the powerful **_Automatic Differentiation_** technology.
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## Procedure
![TONR_formula_linear.png](https://cdn.nlark.com/yuque/0/2022/png/2749792/1667580590971-f4e8f954-a8ce-4a6f-b504-8dd29da793c4.png#averageHue=%23000000&clientId=ua5033e87-1d9a-4&crop=0&crop=0&crop=1&crop=1&from=ui&id=udccf2382&margin=%5Bobject%20Object%5D&name=TONR_formula_linear.png&originHeight=572&originWidth=1711&originalType=binary&ratio=1&rotation=0&showTitle=false&size=37273&status=done&style=none&taskId=uf5b76265-56be-40b3-8de2-7e0be1a02ef&title=)<br />Fig 1. The procedure of AuTONR, taking the stiffness optimization of the linear elastic model as an example.
![TONR_formula_linear.png](https://www.osredm.com/attachments/entries/get_file?download_url=https://osredm.com/repo/idrl/AuTONR/raw/branch/master/Linear_TO/image/TONR_formula_linear.png)<br />Fig 1. The procedure of AuTONR, taking the stiffness optimization of the linear elastic model as an example.
![TONR_Network.png](https://cdn.nlark.com/yuque/0/2022/png/2749792/1667579895206-092a68b8-95f2-43fa-9eb1-3c7fe8a44913.png#averageHue=%23190d05&clientId=ua5033e87-1d9a-4&crop=0&crop=0&crop=1&crop=1&from=ui&id=ub6e7ca67&margin=%5Bobject%20Object%5D&name=TONR_Network.png&originHeight=593&originWidth=1943&originalType=binary&ratio=1&rotation=0&showTitle=false&size=105186&status=done&style=none&taskId=u6fd64eb9-ae53-40ea-9587-2de67e727e4&title=)<br />Fig 2. The architecture of the neural network.
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