In structural optimization, data-driven surrogate models are often explored as alternatives to finite element analysis to reduce computational cost. However, conventional neural networks usually fail to capture key structural characteristics and are limited to predicting global responses (e.g., top displacement), but usually fail to achieve accurate internal force predictions with conventional training data volumes. As a result, most existing studies involving surrogate models did not concern internal force constraints. To address this issue, this study proposes a structural optimization framework based on a pre-trained Physics-Informed Neural Network (PINN) surrogate model. By embedding static equilibrium equation into the loss function, the model achieves higher predictive accuracy, particularly for internal forces, while pre-training accelerates convergence and enhances stability. Combined with an improved multi-swarm particle swarm optimization (MPSO) algorithm, the framework enables efficient optimization of multi-story frame structures under internal force and multiple other constraints. The application to a six-story frame structure validates its effectiveness: compared with a DNN-based model, the PINN-based model improves the coefficient of determination for internal force prediction from 0.8874 to 0.9937. These results demonstrate that the proposed method offers a promising approach for efficient optimization of multi-story frame structures.
Xu et al. (Thu,) studied this question.