<p>This study presents a comprehensive time-dependent electromechanical analysis of functionally graded piezoelectric (FGP) composite panels resting on concrete auxetic foundations, subjected to aerodynamic flow. The investigation integrates advanced theoretical, numerical, and machine learning methodologies to capture the coupled behavior of smart structures under transient loading. A refined higher-order shear deformation theory (HSDT) is employed to model the mechanical behavior of the FGP panel, ensuring an accurate representation of through-thickness deformation without requiring shear correction factors. The electromechanical coupling is governed by Maxwell’s equations, while Hamilton’s principle is utilized to derive the governing equations of motion. To discretize and solve the resulting time-dependent partial differential equations efficiently, a differential quadrature hierarchical finite element method (DQHFEM) is proposed, in conjunction with the Gauss-Lobatto-Legendre (GLL) quadrature rule to ensure numerical stability and precision. The effect of the auxetic foundation, characterized by negative Poisson’s ratio behavior, is incorporated through a modified elastic foundation model. Aerodynamic loads are modeled using first-order piston theory. To validate the proposed mathematical model and verify its predictive capabilities, a deep neural networks (DNN) is trained on simulation data, showing high accuracy in capturing nonlinear time-dependent responses. Parametric studies are conducted to examine the influence of material gradation, aerodynamic intensity, and foundation characteristics on the dynamic response. The results demonstrate the robustness and accuracy of the proposed framework, suggesting its potential for optimizing smart composite structures in aeronautical and civil engineering applications under complex loading environments.</p>