Due to its unique magnetic circuit structure， the synchronous reluctance motor （SynRM） exhibits significant cross-saturation effects during operation， posing challenges for accurate control and performance optimization of the motor.This paper presents a method for identifying cross-saturation characteristic parameters and an improved mathematical modeling method for the nonlinear changes in SynRM parameters caused by magnetic circuit self-saturation and cross-saturation in the static state of the motor. Offline stand still tests are conducted to acquire characteristic data of the motor under different saturation levels. Subsequently， neural networks learn the complex relationships between input currents and output flux linkages， while numerical optimization techniques refine the extracted parameters to minimize model discrepancies. These identified parameters are then integrated into an enhanced mathematical model that effectively incorporates cross-saturation effects. The accuracy and effectiveness of the proposed model are rigorously validated through comprehensive comparisons with finite element analysis （FEA） results and further simulations.