Deep Learning and Transformer Models for Groundwater Level Prediction in the Marvdasht Plain: Protecting UNESCO Heritage Sites--Persepolis and Naqsh-e Rustam  
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1 Hangzhou International Innovation Institute, Hangzhou 310000, China; [EMAIL_ADDRESS]  
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1 Hangzhou International Innovation Institute, Hangzhou 310000, China; [EMAIL_ADDRESS]  
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4 Geological Survey, Tehran 1193653471, Iran; [EMAIL_ADDRESS]; [EMAIL_ADDRESS] (T.Y. ); hab  
among other fields [1, 2]. Its overexploitation--exacerbated by climate change, urbanization, and agricultural expansion--has led to severe groundwater depletion [3] in many regions. This, in turn, has triggered land subsidence [1, 3, 4, 5], threatening global sustainability [6]. The consequences include irreversible loss of aquifer storage capacity, the formation of earth fissures, structural damage to buildings and infrastructure, and an increased risk of flooding owing to soil compaction and induced permeability [7]. In the coming decades, rising global population and economic expansion will drive higher groundwater consumption, intensifying groundwater depletion [1, 7]. When compounded by drought conditions in arid and semi-arid regions, these factors are likely to accelerate land subsidence and amplify its associated damages and consequences [8]. This is particularly alarming in areas of cultural and historical significance, where groundwater management is essential for human and environmental needs and for preserving valuable heritage sites [9, 10, 11, 12]. Persepolis and the Naqsh-e Rustam regions, UNESCO World Heritage sites, exemplify this dual challenge, as aquifer depletion and land subsidence pose direct risks to the archaeological remains. Addressing these interconnected issues requires the integration of cutting-edge remote sensing and computational methods [13], coupled with sustainable management practices [14, 12, 15]. Advances in geodetic-based [1] and machine learning-based methods [2] are transforming groundwater monitoring and modeling. Remote sensing techniques, such as interferometric synthetic aperture radar (InSAR) and gravity recovery and climate experiment (GRACE) satellite data [6], have emerged as vital tools for quantifying ground deformation and regional water storage anomalies [16, 17]. When combined with machine learning frameworks, these datasets provide high-resolution insights into aquifer behavior, especially [18, 19]. Deep learning approaches, such as convolutional neural networks (CNNs) and long short-term memory (LSTM) models, have shown exceptional promise in enhancing groundwater level predictions by leveraging multivariate environmental data [12, 20, 21]. Nevertheless, models like CNNs and LSTMs have limitations when dealing with long-term time series data [2]. CNNs, while effective for spatial pattern recognition [12], are less appropriate for capturing long-range spatial dependencies between hydrological features [2]. LSTMs, designed to handle sequences, can struggle with very long-term dependencies owing to issues like vanishing gradients. Additionally, they are computationally demanding for long sequences and may not perfectly capture the cyclical and trending fluctuations in time-series data [19, 22]. To address these challenges, transformer architectures have been introduced, which replace recurrence with multihead self-attention mechanisms [23, 24, 25, 26]. This allows transformers to model global context directly and handle long sequences more efficiently by processing the entire sequence in parallel. In the context of hydrological sequence modeling, the attention mechanisms enable the model to focus on relevant time steps, such as periods of significant rainfall or pumping activities, which are crucial for accurate groundwater level predictions. Variants like the temporal fusion transformer [27] incorporate interpretable static-context gating, while the Informer [28] uses probabilistic-sparse attention to reduce memory complexity, making it feasible to forecast over extended horizons.