<p>This study investigates the thermal buckling behavior of functionally graded microplates reinforced with graphene, incorporating two piezoelectric layers, resting on an elastic foundation, and subjected to an externally applied voltage. An artificial neural network (ANN) is utilized to analyze this behavior. The governing equations are formulated based on the modified couple stress theory to account for microscale effects. The material properties of the graphene-reinforced composite layer are determined using the Halpin–Tsai micromechanical model. The Ritz method is employed to solve the governing equations and generate the dataset for training the ANN. Specifically, the Levenberg–Marquardt algorithm is implemented within the ANN framework to significantly reduce computational costs in the buckling analysis. The input parameters include nanofiller dimensions, weight fraction, and piezoelectric layer thickness, while the output is the thermal buckling load. The results demonstrate that ANN-based predictions of the critical buckling temperature for functionally graded graphene-reinforced microplates with piezoelectric layers not only achieve high accuracy but also substantially decrease computational time compared to conventional numerical approaches. The obtained results denote that aspect ratio has the most significant impact on critical buckling temperature, with longer plates showing much greater resistance to buckling. Also, elastic foundation stiffness also plays a moderate but important role, particularly at higher stiffness values. In addition, the X pattern is the most effective in enhancing buckling resistance, but the differences between patterns are relatively small.</p>