Dynamically configured physics-informed neural network in topology optimization applications

Abstract

The integration of physics-informed neural network (PINN) and topology optimization (TO) is an attractive issue because PINN can avoid the prohibitive data acquisition of solving forward problems compared to traditional machine learning. To enhance the efficiency of this integrated optimization framework, a dynamically configured PINN-based topology optimization (DCPINN-TO) method is proposed in conjunction with an active sampling strategy. The DCPINN comprises two sub-networks with distinct training costs, capable of dynamically adjusting the trainable parameters based on the optimization state of TO. Moreover, the active sampling strategy selectively samples collocations based on the pseudo-densities, which can significantly reduce training costs by decreasing the number of input collocations. Additionally, the Gaussian integral is used to calculate the strain energy of elements to decouple the mapping of the material at the collocations. The proposed method is extended to various scenarios, including those with high resolution, multiple loads, and displacement constraints. Its efficiency and generalization are validated by several illustrative examples. Furthermore, the accuracy of DCPINN versus finite element analysis-based TO (FEA-TO) was also investigated.