基于深度神经网络的拓扑结构Optimization参数水平集方法（DNN）
A Parametric Level Set Method for Topology Optimization based on Deep Neural Network (DNN)
摘要：
提出了一种基于深度神经网络（DNN）的参数化水平集拓扑优化方法。该方法将全连接深度神经网络与传统的水平集方法相结合，构建了一种有效的结构拓扑优化方法。水平集的隐函数由全连接深度神经网络描述。提出了一种基于DNN的水平集最优化方法，将Hamilton-Jacobi偏微分方程（PDE）转化为参数化的常微分方程（ODE）。通过更新网络的权值和偏置值来更新隐函数的零水平集。周期性地应用参数化重新初始化以防止隐函数在其零水平集附近太陡或太平坦。所提出的方法是在最小顺应性的框架中实现的，这是一个著名的拓扑优化基准。在实践中，设计师希望有多个设计选项，在那里他们可以选择一个更好的概念设计的基础上，他们的设计经验。基于DNN的水平集方法的主要优点之一是它能够生成具有不同网络架构的多样化和有竞争力的设计。数值算例验证了所提出的基于DNN的水平集方法的有效性。
英文摘要：
This paper proposes a new parametric level set method for topology optimization based on Deep Neural Network (DNN). In this method, the fully connected deep neural network is incorporated into the conventional level set methods to construct an effective approach for structural topology optimization. The implicit function of level set is described by fully connected deep neural networks. A DNN-based level set optimization method is proposed, where the Hamilton-Jacobi partial differential equations (PDEs) are transformed into parametrized ordinary differential equations (ODEs). The zero-level set of implicit function is updated through updating the weights and biases of networks. The parametrized reinitialization is applied periodically to prevent the implicit function from being too steep or too flat in the vicinity of its zero-level set. The proposed method is implemented in the framework of minimum compliance, which is a well-known benchmark for topology optimization. In practice, designers desire to have multiple design options, where they can choose a better conceptual design base on their design experience. One of the major advantages of DNN-based level set method is its ability to generate diverse and competitive designs with different network architectures. Several numerical examples are presented to verify the effectiveness of the proposed DNN-based level set method.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
