A coupled thermodynamic-dynamic model of a γ-type free-piston Stirling engine is developed using SAGE software to analyze impedance characteristics and predict output performance by applying two neural network algorithms. The model accounts for four key thermodynamic and dynamic parameters. These parameters determine acoustic impedance, output power, and efficiency. The results show that as a charge pressure is 2.0 MPa, increasing the porosity from 0.86-0.93 leads to output power and efficiency increased from 22.17-35.12 W and the efficiency increased from 18.44%-23.26%. At a charge pressure of 2.5 MPa, as the spring stiffness of the piston rises from 1.0×−3.384× 10^{4} −1.7×-3.384×104 N/m, the real part of the acoustic impedance increases from 3.374×107-3.384×107 Pa·s/m and the virtual part of the acoustic impedance decreases from 1.343×107-1.320×107 Pa·s/m. Furthermore, the study employs a CNN algorithm to predict efficiency and output power, comparing its performance with that of an ANN algorithm. The CNN model demonstrates exceptional predictive accuracy, achieving an R2 value above 0.99 and a mean squared error below 2. This study demonstrates the effectiveness of integrating deep learning with simulation-based modeling to enable rapid and accurate performance prediction, offering a scalable approach for the design optimization of FPSE systems in energy applications.