Recently, artificial intelligence and machine learning are actively discussed in the particle accelerator community. The physics-informed neural network (PINN) method, which is a powerful approach for solving differential equations with deep neural networks (DNN), has been successfully applied to the calculation of electromagnetic fields and beam coupling impedances in particle accelerators. In this work, a hybrid PINN method combined with the boundary integral equation (BIE) method is developed to calculate the fields and impedances in accelerator vacuum chambers at cryogenic temperature. The surface impedance boundary condition for the anomalous skin effect is included to model the electromagnetic characteristics of chamber wall surfaces. Transfer learning can accelerate training processes for DNN parameters in a wide frequency band. The hybrid PINN-BIE approach is verified through applications to various chamber cross sections.