## 5 Conclusions  
Our integration of SBAS-InSAR data with monthly multisource geoinformation layers provides the first sub-decadal (2015-2022) assessment of groundwater dynamics at a 30 m spatial resolution beneath the Perseopolis and Naqsh-e Rustam UNESCO World Heritage complexes. Among the evaluated models, the convolution-enhanced Transformer demonstrates superior performance, explaining approximately 83% (R\({}^{2}\approx\) 0.83) of the variance in blind-well validations and significantly reducing prediction errors to RMSE \(\approx\) 6 m, MAE \(\approx\) 4 m, and MAPE \(\approx\) 12%. Compared to a CNN-LSTM baseline (RMSE \(\approx\) 13 m; R\({}^{2}\approx\) 0.44), this approach reduces prediction error by more than half, and compared to a vanilla LSTM model (R\({}^{2}\approx\) 0.28), it nearly triples the variance explained. Furthermore, over 90% of absolute prediction errors remain below 15 m, with residuals closely distributed around zero. Conversely, the sparsity-optimized Informer explains only about 40% of the variance, retaining an RMSE greater than 13 m. This discrepancy highlights the effectiveness of dense convolutional attention mechanisms when modeling geophysically complex and high-dimensional time series. According to international guidelines, such as those from the International Council on Monuments and Sites (ICOMOS), land subsidence poses a significant threat to the structural integrity of stone heritage movements, potentially causing irreversible cracking or collapse. Our observed and model-predicted subsidence rates exceeding 180 mm per year underscore a clear and immediate risk to the Perseopolis stone carvings and associated heritage elements. Across eight years of monthly observations, all Transformer variants--standard, convolutional, and sparse--consistently outperform recurrent architectures (LSTM, bi-LSTM, and CNN-LSTM) in terms of accuracy, bias, and residual structure. Multi-head self-attention preserves long-range dependencies without vanishing gradients, while sparse attention mechanisms scale efficiently across thousand-step horizons, an essential property for modeling long eco-hydrological archives. Feature attribution reveals that InSAR velocity, NDVI, GPP, and slope aspect jointly account for 51% of the model's explanatory power, highlighting the importance of vegetation productivity and terrain morphology in encoding the hydrological memory needed for sustainable-use forecasting. Transformers effectively map these complex ecological signals to groundwater-level predictions with minimal phase drift by explicitly learning their latent couplings. This modeling framework enables early warning of cultural heritage risks by identifying subsidence hotspots exceeding -180 mm\(\cdot\)yr\({}^{-1}\), which co-occur with groundwater storage losses of 4-6 m\(\cdot\)yr\({}^{-1}\). Extrapolation suggests vertical displacement could exceed 200 mm\(\cdot\)yr\({}^{-1}\) within a decade, posing a direct threat to the Achaememid stone reliefs unless groundwater abstraction is significantly reduced. Attention-based saliency maps also highlight irrigation-induced stress periods that are obscured in recurrent baselines, facilitating transparent communication with water authorities. Despite the robust performance of the proposed Transformer-based framework, several limitations warrant attention. First, while the dataset used for training covers a wide range of environmental variables, it may not fully capture the physical complexity of subsurface hydrology in the Marvdasht Plain. Second, InSAR-derived vertical motion was not directly validated with dense in situ measurements such as global navigation satellite system (GNSS) or extensometers due to data scarcity, which may affect the precision of subsidence-groundwater correlations. Third, the GRACE TWSA signal integrates over large spatial footprints, limiting the model's ability to resolve fine-scale storage anomalies.