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Generative adversarial network guided topology optimization of periodic structures via Subset Simulation

机译：通过子集模拟的经常性逆境网络引导拓扑优化周期性结构的优化

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摘要

Topology optimization offers great potential to design periodic structures with desired bandgap properties. This paper proposes a novel Subset Simulation (SS) based topology optimization framework by integrating SS with generative adversarial network (GAN). First, the topology optimization problem is reformulated as a rare event simulation problem in reliability analysis, where the optimal solutions are analogously the rare event samples close to failure. Then SS, which has been developed for efficient simulation of rare events in reliability analysis, is used to effectively find the optimal topologies. In each iteration of SS, to address the challenge of simulating samples from high-dimensional design space (stemming from discretization of the unit cell to represent different topologies), this paper proposes to use GANs to learn an implicit model for the underlying high-dimensional failure distribution based on existing failure samples (i.e., topologies with higher objective function values) from the previous iteration in SS, and then use the trained GANs to directly and efficiently generate failure samples (i.e., new promising topologies). Overall, the proposed SS-based and GAN-guided topology optimization algorithm can facilitate efficient topology optimization of periodic structures. The effectiveness and efficiency of the proposed approach are demonstrated through topology optimization of 2D periodic structures.
机译：拓扑优化提供了设计具有所需带隙属性的定期结构的潜力。本文通过将SS与生成的对抗网络（GAN）集成来提出基于基于拓扑优化框架的新型子集仿真（SS）。首先，拓扑优化问题被重构为可靠性分析中的罕见事件仿真问题，其中最佳解决方案类似于难以发生故障的罕见事件样本。然后，已经开发了用于高效模拟可靠性分析中罕见事件的SS，用于有效地找到最佳拓扑。在SS的每次迭代中，解决模拟来自高维设计空间的样本的挑战（从单元电池的离散化代表不同拓扑的离散化），提出使用GAN来学习底层高维的隐式模型从SS中的先前迭代，基于现有故障样本（即，具有较高目标函数值的拓扑）的故障分布，然后使用训练的GAN直接和有效地生成失败样本（即新的有前途拓扑）。总的来说，所提出的SS为基础和GAN引导的拓扑优化算法可以促进周期性结构的高效拓扑优化。通过2D周期性结构的拓扑优化来证明所提出的方法的有效性和效率。

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