The reduced-order-model(ROM) method provides a strong support for the rapid iteration and simulation verification of supporting fluid system design. This study focuses on the problems of gradient disappearance or explosion and incomplete learning of flow field characteristics in the training process of PINN ROM. Based on PINN model, an innovative ROM Res-PINNs is proposed. By embedding ResNet module into PINN neural network structure, it strives to improve the training stability of the model while retaining physical knowledge. In addition, parallel network structure is added to the model to improve its perception and learning ability of flow field state.At last, in order to verify the validity of the proposed model, two classical fluid problems, the flow around a cylinder and Vortex-Induced Vibration(VIV), are selected to compare and verify the proposed Res-PINNs model. The results show that Res-PINNs can reconstruct the flow field state more accurately, effectively overcome the problems of gradient disappearance or explosion and poor learning ability of PINN model during training, and provide a new solution for the application of deep learning order reduction method in aerospace system modeling and simulation.