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<p>This paper introduces two novel methods: gradient online learning and prediction (GoLap) and stochastic gradient online learning and prediction (SGoLap) for accelerating the topology optimization using level-set method (LSM). The GoLap and SGoLap methods utilize neural networks and recurrent neural networks to learn and predict topological derivatives online, reducing the need for repetitive FEA and sensitivity computations in the iterative optimization process. Using the new methods, the topological derivatives calculated and predicted in the previous and current iterations are used as training samples. Specifically, the GoLap and SGoLap use the full vectors and the stochastically selected subset of the topological derivatives as training samples respectively. By integrating these methods into LSMs using a reaction–diffusion equation, the total computational time is significantly reduced by up to 98.5% when solving the considered 2D and 3D topology optimization problems.</p>

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Accelerating level-set based topology optimization using gradient and stochastic gradient online learning and prediction methods

  • 期刊论文

  • 发表日期：

    2025年6月27日

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  • Yi Xing,
  • Takayuki Yamada,
  • Liyong Tong

摘要

This paper introduces two novel methods: gradient online learning and prediction (GoLap) and stochastic gradient online learning and prediction (SGoLap) for accelerating the topology optimization using level-set method (LSM). The GoLap and SGoLap methods utilize neural networks and recurrent neural networks to learn and predict topological derivatives online, reducing the need for repetitive FEA and sensitivity computations in the iterative optimization process. Using the new methods, the topological derivatives calculated and predicted in the previous and current iterations are used as training samples. Specifically, the GoLap and SGoLap use the full vectors and the stochastically selected subset of the topological derivatives as training samples respectively. By integrating these methods into LSMs using a reaction–diffusion equation, the total computational time is significantly reduced by up to 98.5% when solving the considered 2D and 3D topology optimization problems.