This paper proposed a new topology optimization method based on geometry deep learning. The density distribution in design domain is described by deep neural networks. Compared to traditional density-based method, using geometry deep learning method to describe the density distribution function can guarantee the smoothness of the boundary and effectively overcome the checkerboard phenomenon. The design variables can be reduced phenomenally based on deep learning representation method. The numerical results for three different kernels including the Gaussian, Tansig, and Tribas are compared. The structural complexity can be directly controlled through the architectures of the neural networks, and minimum length is also controllable for the Gaussian kernel. Several 2-D and 3-D numerical examples are demonstrated in detail to demonstrate the effectiveness of proposed method from minimum compliance to stress-constrained problems.

中文翻译：

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基于深度表示学习 (DRL) 的拓扑优化，用于合规性和应力约束设计

本文提出了一种基于几何深度学习的拓扑优化新方法。设计领域的密度分布由深度神经网络描述。与传统的基于密度的方法相比，使用几何深度学习方法来描述密度分布函数，可以保证边界的平滑性，有效克服棋盘格现象。基于深度学习表示方法可以显着减少设计变量。比较了包括 Gaussian、Tansig 和 Tribas 在内的三种不同内核的数值结果。结构复杂度可以通过神经网络的架构直接控制，最小长度也可以通过高斯核来控制。