Accurate dynamics modeling of aerial manipulators is challenging because platform--manipulator coupling, history-dependent interactions, and changing payload or manipulator configurations produce cross-coupled, temporal, and nonstationary residual dynamics. We propose a structured encoder--decoder framework in which a nonlinear history encoder captures temporal and cross-variable dependencies, while a lightweight linear latent decoder supports efficient deployment-time adaptation. Its linear-in-parameter structure enables closed-form Bayesian updates with consistency-driven covariance inflation and integration with real-time model predictive control (MPC). Experiments on a real aerial-manipulation platform demonstrate improved residual-prediction accuracy, rapid adaptation following dynamics changes, and lower MPC tracking error under changing payload conditions. The results show that combining structured history-dependent representation learning with lightweight online adaptation provides an effective predictive model for aerial manipulation under coupled and nonstationary dynamics.

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