The precise energy and temporal control advantages of the 2 µm double-pulse laser have diverse applications in laser processing, biomedicine, and communications. The Ho: YAP Q-switched double pulse laser, a complex system, demands comprehensive theoretical analysis and precise experimental operations, especially when managing pulse overlap and ensuring output stability. Traditional design methods, time-consuming and labor-intensive, pose challenges in error elimination and susceptibility to environmental and device instabilities. This paper focuses on regulating the design and performance of the Ho: YAP Q-switched double-pulse laser. Critical developmental and optimization challenges are addressed by utilizing a back propagation neural network to forecast the nonlinear propagation of the laser while affirming the feasibility of bypassing intricate numerical solution models. This strategy streamlines experimental trials, ensuring reliable predictions of laser output characteristics and laying the foundation for forecasting more intricate laser systems in the future.