Risk Dynamic Evolution Model of Pension Financial System based on Partial Differential Equation from the Perspective of Complex Network

With the increasing trend of global population aging, traditional risk assessment methods often overlook the nonlinear interactions and dynamic feedback mechanisms between various elements in the system, making it difficult to capture the complex process of risk evolution. This study identified and characterized the complex relationships between participants in the pension financial system through complex network analysis, including fund flows, policy impacts, market fluctuations, and other dimensions. Then, partial differential equations (PDEs) were introduced as the core modeling tool, and a pension financial system based on partial differential equations (PFS-PDE) risk dynamic evolution model was established by combining PDEs. The PFS-PDE model achieved a relatively high intersection over union (IOU) value after fewer training iterations (about 30) and remained relatively stable thereafter, indicating that the model has a fast convergence speed. The PFS-PDE model has relatively low mean square error (MSE) values and a relatively small fluctuation range under most training iterations, which can be considered as a relatively better performance. Compared with other models, the PFS-PDE model has a smaller range of MSE value fluctuations, indicating that the model has high stability during the training process.