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<p>The physical informed neural network (PINN) has attracted significant interest in the field of topology optimization in recent years. By incorporating physical information into the loss function, the process of the neural network’s loss decreasing is equivalent to the process of approximating the solution of the physical equation. In particular, the loss function can be combined with the objective function in topology optimization. This paper proposes a nested PINN framework based on the level set method (LSM), called LSM-PINN. The key of this framework lies in the algorithm transformation from LSM to PINN. Conventional topology optimization method is based on boundary evolution and may lead to a too scattered structure. In order to reduce this problem in PINN, some restrictions are proposed. During the optimization process, the design domain is discretized into several sample points to participate in the network training. Moreover, the feasibility and potential of the LSM-PINN framework are evaluated through some cases, highlighting the advantages and limitations of the LSM-PINN framework. The results show that the LSM-PINN framework proposed can solve two-dimensional topology optimization problems relatively stably and significantly reduce the dependence on the initial design.</p>

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A new level set structual topology optimization framework enhanced by nested physical informed neural network

  • 期刊论文

  • 发表日期：

    2026年5月7日

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  • Boxue Wang,
  • Xihua Chu,
  • Hui Liu

摘要

The physical informed neural network (PINN) has attracted significant interest in the field of topology optimization in recent years. By incorporating physical information into the loss function, the process of the neural network’s loss decreasing is equivalent to the process of approximating the solution of the physical equation. In particular, the loss function can be combined with the objective function in topology optimization. This paper proposes a nested PINN framework based on the level set method (LSM), called LSM-PINN. The key of this framework lies in the algorithm transformation from LSM to PINN. Conventional topology optimization method is based on boundary evolution and may lead to a too scattered structure. In order to reduce this problem in PINN, some restrictions are proposed. During the optimization process, the design domain is discretized into several sample points to participate in the network training. Moreover, the feasibility and potential of the LSM-PINN framework are evaluated through some cases, highlighting the advantages and limitations of the LSM-PINN framework. The results show that the LSM-PINN framework proposed can solve two-dimensional topology optimization problems relatively stably and significantly reduce the dependence on the initial design.