  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.
