To improve the accuracy of simulating unsteady hydrodynamic processes in compound river channels, a method for simulating unsteady flows in compound river channels based on physics-informed neural networks (PINNs) was proposed. The Saint-Venant equations and the 1D+ model were incorporated as physical constraints into the deep learning framework to construct a PINN model for simulating compound scenarios with overlapping flood peaks and storm surges. In addition, a transfer learning strategy was designed to achieve migration from rectangular river channels to compound river channels, and a dual-optimizer training scheme combining Adam and SGD was developed. The verification results of the example show that the proposed PINN model can effectively capture the hydraulic interactions between the river channel and floodplain, with a 31.8% improvement in prediction accuracy compared to traditional methods (RMSE is reduced from 0.085 m to 0.058 m). The transfer learning strategy based on pretraining in rectangular river channels can significantly improve the model performance, with the RMSE reduced by 34.5%; the training strategy using both Adam and SGD optimizers effectively suppresses overfitting, increasing the model’s prediction accuracy by 32.5%.