Abstract: The radiation noise induced by structural vibration is a key issue in the field of noise control. Accurate prediction of the radiated acoustic field is crucial for taking appropriate noise control measures. However, in practical engineering, it is difficult to directly obtain the global true values of structural vibration responses due to limitations in measurement environment and cost. Moreover, the prediction accuracy of traditional numerical methods is limited when the observation data is limited. Firstly, taking the forced vibration process of a rectangular plate as an example and combining it with the numerical calculation process of acoustic radiation problems, this paper shows that accurately reconstructing the vibration response as much as possible is the key to improving the prediction accuracy of the radiated acoustic field when the observation points are limited. Subsequently, this paper proposes a method based on Physics-Informed Neural Networks (PINNs) to reconstruct the global response of structural vibration from limited observation data, thereby improving the prediction accuracy of the radiated acoustic field. During the training process of PINNs, appropriate data preprocessing and activation function selection effectively alleviate the problems of unbalanced loss terms and optimization difficulties of high-order gradients. Simulation results show that the prediction accuracy of the radiated acoustic field using the proposed method is better than that of methods without reconstruction and those based on surface interpolation of the structure. In addition, the proposed method has good robustness for the reconstruction of structural vibration responses under different boundary constraints.