Continuous monitoring of large structures is crucial to ensure their optimal functionality. This paper presents a comprehensive study on dam monitoring using the interferometric synthetic aperture radar (InSAR) technique and prediction time series based on InSAR data. Two types of dams were the focus of the study: rock-fill Atatürk Dam, the largest dam in Türkiye, located in the eastern part of the country, and earth-fill Büyükçekmece Dam in Istanbul. In our analysis, we applied the compressed InSAR approach, which provides a higher density of persistent scatter for InSAR analysis. Unlike other studies on dam monitoring using InSAR methods, we aimed to predict displacement using time series derived from both ascending and descending InSAR results, yet this aspect has received little attention. For this purpose, we employed the long short-term memory (LSTM) neural network deep learning method. Moreover, we conducted experiments in both dams with different training and testing ratios acquired in both ascending and descending orbits to evaluate the importance of sampling number. The maximum displacements observed were −15 mm/year for Büyükçekmece Dam and −7 mm/year for Atatürk Dam. For Atatürk Dam, the root-mean-square error (RMSE) is consistently less than 0.9 mm, with percent root-mean-square error (%RMSE) ranging between 6.9% and 26%. In the case of Büyükçekmece Dam, we observed an RMSE of less than 1.3 mm, with %RMSE values ranging between 9.3% and 36.5% for different training and testing scenarios. Our LSTM results demonstrated that as the training percentage increased, the %RMSE values generally lose as well. This indicates a considerably higher relative error when less training data are used, highlighting the importance of data quantity in the predictive accuracy of our model. The results demonstrated that the LSTM estimation method can be effectively applied to health monitoring of large structures, such as dams.