Abstract: To address the difficulties in obtaining full-field dynamic responses of complex truss structures under sparse monitoring conditions, the high online computational cost of conventional finite element methods, and the insufficient physical consistency of purely data-driven models, this study proposes a full-field response reconstruction and parameter identification framework that integrates proper orthogonal decomposition (POD), a physics-informed long short-term memory network (PI-LSTM), and sparse monitoring data. The proposed framework is termed a Sparse Physics-Informed Network based on Long Short-Term Memory, namely SPIN-LSTM. In the offline stage, full-field response snapshots generated by finite element analysis are used to construct the POD basis, through which high-dimensional structural dynamic responses are mapped onto a low-dimensional modal space. The reduced-order dynamic equations are then formulated and embedded into the PI-LSTM network, thereby reducing computational complexity while ensuring physical consistency. In the online prediction stage, SPIN-LSTM takes limited monitoring-point data and external environmental information as network inputs to predict the responses of all structural members, and identifies structural stiffness and external loads by minimizing the observation error and physics residuals. Numerical examples on truss structures show that the proposed framework can accurately capture the time-history evolution of structural dynamic responses and achieves high reconstruction accuracy at both monitored and unmonitored points. The parameter inversion results indicate that the method can effectively identify structural stiffness and ice thickness while maintaining good inversion stability and noise robustness under different noise levels. In addition, a bridge structure example is introduced to verify the generalization capability of the method under different structural topologies and boundary conditions. Finally, ablation studies further demonstrate the synergistic contribution of reduced-order modeling, temporal modeling, and physics-informed constraints to model performance. Overall, the SPIN-LSTM framework provides an efficient and generalizable solution for structural dynamic response prediction and parameter identification under sparse monitoring conditions, showing promising application potential in digital twin modeling and health monitoring of truss structures.