Neural networks, and more broadly, machine learning techniques, have been recently exploited to accelerate topology optimization through data-driven training and image processing. In this paper, we demonstrate that one can directly execute topology optimization (TO) using neural networks (NN). The primary concept is to use the NN’s activation functions to represent the popular Solid Isotropic Material with Penalization (SIMP) density field. In other words, the density function is parameterized by the weights and bias associated with the NN, and spanned by NN’s activation functions; the density representation is thus independent of the finite element mesh. Then, by relying on the NN’s built-in backpropogation, and a conventional finite element solver, the density field is optimized. Methods to impose design and manufacturing constraints within the proposed framework are described and illustrated. A byproduct of representing the density field via activation functions is that it leads to a crisp and differentiable boundary. The proposed framework is simple to implement and is illustrated through 2D and 3D examples. Some of the unresolved challenges with the proposed framework are also summarized.

神经网络，更广泛的说是机器学习技术，最近已被利用来通过数据驱动的训练和图像处理来加速拓扑优化。在本文中，我们证明了可以使用神经网络（NN）直接执行拓扑优化（TO）。主要概念是使用NN的激活函数来表示流行的带有罚分的固体各向同性材料（SIMP）密度字段。换句话说，密度函数由与NN相关的权重和偏差参数化，并由NN的激活函数进行扩展；因此，密度表示独立于有限元网格。然后，依靠NN内置的反向传播和传统的有限元求解器，可以优化密度场。描述和说明了在建议的框架内施加设计和制造约束的方法。通过激活函数表示密度场的副产品是，它导致了清晰易辨的边界。所提出的框架易于实现，并通过2D和3D示例进行了说明。还总结了所提出框架的一些未解决的挑战。