Revealing the coupling mechanism between the nonlinear effect and the multi-physical fields in the bistable plate, as well as the interaction between multiple impacts, promotes the innovative development of morphing structures. Improved neural network technology contributes to the adaptive design and functional integration of morphing structures. The multiple impacts of functional gradient magneto-electro-elastic (FG-MEE) plates with convex and concave configurations are investigated. In the Reddy high-order shear plate theory considering the bistable configuration, functional gradient models and magneto-electro-mechanical effect models are constructed. To measure the contact forces in the multi-impact process, the modified Hertz contact model is introduced. Through the Hamiltonian variational principle, the nonlinear multiple impact dynamics of the FG-MEE plates with convex and concave configurations are modeled. To obtain the bistable configuration induced by the magneto-electro-mechanical coupling effects, the two-step perturbation method is extended in multiple physical fields. Further, the two-step perturbation method and the Galerkin method are extended to acquire the higher-order truncated solutions for the multiple impact responses of FG-MEE plates with convex and concave configurations. Based on the numerical result database of multiple impact response, the nonlinear mapping relationship between the structure characteristics, load characteristics and multiple impact responses of bistable FG-MEE plate is constructed by the particle swarm optimization-back propagation (PSO-BP) technology. Ultimately, the coupling effects between the multi-physical fields and nonlinear behaviors in FG-MEE plates with convex and concave configurations are comparatively analyzed, and the interactions between multiple impacts are systematically revealed.