A topology description function-enhanced neural network for topology optimization

Topology optimization aims to find an economic and efficient structure with a lighter overall weight. Topology description functions (TDFs), which are an explicit level-set approach for topology optimization, can obtain the explicit structure geometry function of the topology. However, due to the original hard thresholding in the conventional TDF, the TDF is a derivative-free method that requires significant computational resources, which creates barriers to its widespread adoption among structural engineers. To fix this problem, a novel TDF-enhanced neural network (TDF-NN) is proposed, which introduces the sigmoid activation function as soft thresholding to allow the adoption of gradient-based optimization approaches. Meanwhile, TDF-NN uses a single-layer neural network to model the TDF, and the weights of the TDF are converted to the weights of the TDF-NN, which can be obtained directly by optimization instead of solving the linear equations. The performance of the proposed method is validated through the compliance minimization problems and the heat conduction problem, and it definitely can also be used for other topology optimization problems. The computational cost of the proposed method, the effect of the number of knots on TDF-NN, diverse designs, and application to real-life structures are also discussed. These results indicate that the proposed method is a universal topology optimization method. Numerical examples show that the proposed method has higher computational efficiency than the solid isotropic material with penalization method. It has a speedup factor of approximately two to 10 times. Moreover, multiple competitive solutions can be generated by changing the number of knots, which will allow architects to select a suitable structure for the design task.