This study puts forward a logical framework for green innovation network analysis, which includes a spatial dimension, a relational dimension, and a systems dimension. Here, we put forward some basic research ideas concerning the optimization and regulation of green innovation networks in terms of the systems dimension and we investigate the micro-dynamic mechanisms of green innovation network expansion using a spatial econometric model. Our main research results are as follows: The efficiency of green innovation in the Yangtze River Economic Belt has improved significantly, however, the gap between cities has gradually increased, and a problem of efficiency regression has emerged. The green innovation network has changed from the primary stage dominated by Edge Network to the rapid growth stage dominated by Supporting Network, and formed a complex network pattern with diversified hierarchical structure. Node symmetry is helpful in forming more extroverted connections and promoting the expansion of green innovation networks. Node proximity and connection symmetry inhibit the growth and development of networks, and knowledge flow cooperation networks can accelerate the evolution of green innovation networks. Finally, this paper holds that we should combine the actual development needs, emphasize the basic principles of differentiated development, and construct the development pattern of regional collaborative innovation. This can also provide a theoretical reference for enriching our understanding of green innovation networks while narrowing the gap between cities.

With its proposal of the “double carbon” (peak carbon dioxide emissions and carbon neutralization) goal, China has entered a new stage in creating an ecological civilization and achieving sustainable development. Based on the formation and evolution mechanism of the carbon emission efficiency network, in this study, a trilateral evolutionary game model—including efficiency groups (high- and low-efficiency groups) and local governments—was constructed, in an attempt to discuss the conditions needed for different players and trilateral interconnected systems to implement balanced and stable strategies. Furthermore, the sensitivity of the participants’ evolutionary trajectories toward factors such as the initial strategy ratio, transition cost, and network capital were tested via a system simulation. The main conclusions were as follows: (1) Efficiency groups form a virtuous circle when the initial proportion of the participants’ strategies reaches a certain threshold, and converge into a stable “win–win” state. Under these circumstances, high-efficiency groups tend to give full play to their efficiency advantages in terms of carbon emission reduction and green development, while low-efficiency groups tend to choose green transformation and accept the spillover effect from high-efficiency groups. (2) When efficiency groups achieve a “win–win” state or form good self-management, local governments move from active supervision to a passive supervision strategy in order to reduce supervision costs. (3) While different initial strategy proportions do not affect the stable convergence point of the evolutionary system, they have a differentiated impact on the convergence speed of the players. Under the condition of a low initial strategy ratio, transformation costs can reduce the green transformation enthusiasm of inefficient groups, while network capital can enhance the green transformation willingness of inefficient groups.

In the design of fluid systems, rapid iteration and simulation verification are essential, and reduced-order modeling techniques can significantly improve computational efficiency and accuracy. However, traditional Physics-Informed Neural Networks (PINNs) often face challenges such as vanishing or exploding gradients when learning flow field characteristics, limiting their ability to capture complex fluid dynamics. This study presents an enhanced reduced-order model (ROM): Physics-Informed Neural Networks based on Residual Networks (Res-PINNs). By integrating a Residual Network (ResNet) module into the PINN architecture, the proposed model improves training stability while preserving physical constraints. Additionally, the model’s ability to capture and learn flow field states is further enhanced by the design of a symmetric parallel neural network structure. To evaluate the effectiveness of the Res-PINNs model, two classic fluid dynamics problems—flow around a cylinder and Vortex-Induced Vibration (VIV)—were selected for comparative testing. The results demonstrate that the Res-PINNs model not only reconstructs flow field states with higher accuracy but also effectively addresses limitations of traditional PINN methods, such as vanishing gradients, exploding gradients, and insufficient learning capacity. Compared to existing approaches, the proposed Res-PINNs provide a more stable and efficient solution for deep learning-based reduced-order modeling in fluid system design.

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.