Landslide displacement prediction and interpretability analysis based on a graph spatiotemporal attention network

Abstract

Accurate prediction of landslide displacement is central to early warning of geological disasters, yet existing data-driven models predominantly employ convolutional neural networks on regular grids, which fail to match the irregular spatial distribution of actual monitoring points and lack physical interpretability. In this paper, we propose a Graph Spatio-Temporal Attention Network (GSTA-Net) that uses a graph convolutional network to model the spatial structure of irregularly distributed monitoring points, employs an LSTM with a temporal attention mechanism to capture the dependencies of rainfall and reservoir water level, and visualizes spatial and factor attention weights to reveal deformation patterns and the dynamic evolution of dominant triggering factors. Using the Baishuihe landslide in the Three Gorges Reservoir area as a case study, we train and validate the model on displacement data from monitoring point ZG118 and synchronous rainfall and reservoir water level data from 2006 to 2012. On the 2012 test set, GSTA-Net achieves an RMSE of 11.38 mm and a MAPE of 4.52%; compared with CNN‑LSTM, RMSE and MAPE are reduced by 11.6% and 11.2% respectively; compared with GWO‑SVM, RMSE is reduced by 21.3% and MAPE by 33.8%; and compared with DCRNN, GSTA‑Net reduces RMSE by 5.6% and MAPE by 0.36 percentage points while cutting training time by about 52%. Spatial attention reveals that monitoring points on the middle and rear edge of the landslide contribute the most, consistent with the “progressive retrogressive failure” mechanism, and factor attention shows that during reservoir drawdown (January–June) water level dominates deformation, whereas during the rainy season (July–September) rainfall influence increases significantly with a lag of about 1–2 months, demonstrating that the proposed model enhances both prediction accuracy and physical interpretability.

1 Introduction

Accurate landslide displacement prediction is central to early warning of geological disasters. In the Three Gorges Reservoir area, the combined effect of periodic reservoir water level fluctuations and intense rainfall has reactivated many ancient landslides, which exhibit step-like deformation characteristics (Casagli et al., 2023; Ma et al., 2021a; Zhou et al., 2025). This creates an urgent need for high-accuracy, interpretable prediction models (Ji et al., 2022; Wang Y. et al., 2022; Al-Najjar et al., 2023).

Traditional landslide displacement prediction methods mainly include deterministic physical models and nonlinear data-driven models (Ebrahim et al., 2024; Wang et al., 2024). Deterministic models rely on detailed geomechanical parameters and boundary conditions, making them difficult to apply at large scales or under complex geological conditions. With the development of geotechnical monitoring big data, nonlinear models based on machine learning and deep learning have become mainstream, such as support vector machines (SVM), extreme learning machines (ELM), and long short-term memory (LSTM) networks (Li et al., 2023). These methods can effectively capture the nonlinear mapping between external triggering factors (e.g., rainfall, reservoir water level) and displacement response (Dai et al., 2022). In recent years, data-driven landslide displacement prediction studies can be summarized into three representative categories, each with notable limitations. The first is single-point time-series modeling, such as SVM, LSTM and their variants, which build independent prediction models for each monitoring point. These methods ignore the spatial coupling information among monitoring points and cannot reflect the overall evolution state of the landslide (Teke and Kavzoglu, 2024). The second is spatial modeling on regular grids. A few studies have attempted to interpolate monitoring points onto regular grids and then use convolutional neural networks (CNNs). However, actual landslide monitoring points are irregularly distributed; regular grids disrupt the original spatial topology, reducing feature extraction efficiency (Pradhan et al., 2023). The third is interpretability methods. Post-hoc attribution methods such as SHAP (Shapley Additive Explanations) can quantify feature importance but cannot be embedded into the model training process. Physics-informed neural networks (PINNs) can enforce mechanical consistency but struggle to dynamically capture the time-varying contributions of triggering factors (Maxwell et al., 2021).

Notably, the Transformer architecture, with its multi-head self-attention mechanism for long-range dependency modeling, has recently shown great potential in remote-sensing landslide identification (Jiang et al., 2026). DBSANet, through a dual-branch architecture fusing ResNet and Swin Transformer, achieved IoU values of 77.12% and 75.23% on the Bijie and Luding datasets, respectively (Li Y. et al., 2025). Lights-Transformer, with a lightweight Transformer as its core, reached an mIoU of 85.11% on the GDCLD dataset, combining high accuracy and computational efficiency (Wu et al., 2025). D²FLS-Net, via a DEM-guided dual-stage fusion Transformer, improved mIoU to 88.77% (Li J. et al., 2025). CNN-Transformer hybrid models such as CTHNet improved the F1-score by at least 3.81% over baseline models in loess plateau landslide identification (Zhao et al., 2025). Moreover, methods based on hierarchical cross-attention (e.g., CTL-DETR, CALandDet) and lightweight dual-stream attention networks suitable for edge deployment have further validated the effectiveness of Transformer and hybrid attention architectures for landslide identification from different perspectives (Zang et al., 2025). However, these works mainly focus on static identification and segmentation of landslide areas. The application of Transformer/hybrid attention systems to time-series dynamic prediction of landslide displacement remains relatively limited this is the core issue addressed by the present paper.

Using the Baishuihe landslide in the Three Gorges Reservoir area as an engineering case study, we train, validate, and compare the proposed model using displacement data from monitoring points and synchronous rainfall and reservoir water level data from 2006 to 2012. The results show that GSTA-Net outperforms traditional CNN-LSTM, GWO-SVM, and DCRNN in both prediction accuracy and interpretability.

The remainder of this paper is organized as follows: Section 2 details the principle and structure of the GSTA-Net model, including graph construction, graph convolution operations, dual attention mechanisms, and the prediction output layer. Section 3 introduces the engineering geological conditions of the Baishuihe landslide, the monitoring data, and the modeling steps. Section 4 presents the prediction results, comparative experiments, and attention weight analysis. Section 5 discusses the model applicability, limitations, and future improvements. Section 6 concludes the paper.

2 Model principle

2.1 Landslide displacement prediction model based on Graph Spatio-Temporal Attention Network (GSTA-Net)

FIGURE 1

2.2 Graph convolution module: graph construction and spatial feature extraction

The GPS monitoring points deployed on a landslide body exhibit an irregular spatial distribution, which conventional convolutional neural networks cannot directly process. In this paper, we employ a Graph Convolutional Network (GCN) to model the spatial deformation correlations among monitoring points (Ma et al., 2021b; Chitla et al., 2026). This module consists of two sub-steps: construction of the graph adjacency matrix and graph convolution operations.

2.2.1 Construction of the graph adjacency matrix

The N GPS monitoring points on the landslide body are treated as the node set V (|V| = N) in a graph G = (V, E), and the spatial dependencies between nodes are represented by the edge set E. This paper adopts a graph construction method based on the Euclidean distances between monitoring points. The specific steps are as follows:

Step 1: Compute the distance matrix.

Let the planar coordinates of the ith monitoring point be . Then the Euclidean distance between two points and is Equation 1:

Step 2: Threshold-based Gaussian kernel weighting.

To avoid information redundancy caused by overly dense connections while maintaining graph sparsity, a thresholded Gaussian kernel function is used to compute the elements of the adjacency matrix (Equation 2):

The bandwidth parameter is taken as the standard deviation of the distances between all monitoring points, i.e., . The distance threshold is set to approximately 1.5 times the average distance between monitoring points, so that the graph maintains moderate connectivity. This Gaussian kernel function assigns larger edge weights to nodes that are closer together, while nodes whose distance exceeds the threshold have no direct edge between them.

Step 3: Adding self-loops and symmetric normalization.

To facilitate the aggregation of a node’s own features during graph convolution, self-loops are added following Kipf and Welling (2017), i.e., , where is the identity matrix. Subsequently, symmetric normalization is applied (Equation 3):where is the degree matrix of , i.e., . is the normalized adjacency matrix that is finally input to the graph convolutional layer.

2.2.2 Graph convolution operation

Graph convolution updates the representation of a node by aggregating features from its neighbors, thereby extracting spatial deformation correlations. This paper adopts the first-order approximation graph convolution proposed by Kipf and Welling, whose layer-wise propagation rule is Equation 4:where: is the node feature matrix at layer (with being the original input features); is the learnable weight matrix at layer ; is the activation function (ReLU is used in this paper). By stacking two graph convolutional layers , the receptive field of each node expands to its second-order neighbors, effectively capturing both local and global spatial deformation correlations across the landslide body. The final output of the spatial module is the feature matrix after spatial information integration, where the spatial feature dimension is denoted as (set to 64 in this paper).

The six monitoring points used in this paper (ZG118, ZG093, XD-01, XD-02, XD-03, and XD-04) are all located on the main profile of the Baishuihe landslide or within 50 m on either side of the main profile, and their spatial distribution is essentially aligned with the main sliding direction. Therefore, the graph construction based on Euclidean distance can effectively capture the deformation transfer relationship along the main sliding direction (rear edge → middle-rear edge → front edge).

2.3 Time series processing

2.3.1 Sequence of external triggering factors

The external triggering factors for landslide displacement mainly include rainfall and reservoir water level changes (Ullah et al., 2022). In this paper, the following M = 3 time series are selected as inputs to the temporal module: daily rainfall (, unit: mm); reservoir water level elevation (, unit: m); and reservoir water level change rate (, unit: m/d). Let the time window length be T = 12 months in this paper). The input matrix is then , where each row corresponds to the vector of environmental factors at a given time step.

2.3.2 Factor attention mechanism

The contributions of different external triggering factors to landslide displacement are not constant (Cui et al., 2022). For example, during rapid reservoir water level drawdown, the water level change may become the dominant factor, whereas during the rainy season, the influence of rainfall may be more significant (Xu et al., 2021). The factor attention mechanism aims to dynamically assign weights to each input factor at each time step. At time , given the input factor vector , the attention score for the kth factor is computed using the hidden state and cell state from the previous time step (Equation 5):where , , , and are learnable parameters, and denotes vector concatenation. The factor weights are then obtained by normalization via the Softmax function (Equation 6):

The weighted input vector is Equation 7:

The weighted input vector is then fed into the LSTM unit in place of the original .

2.3.3 Temporal attention mechanism

The response of landslide displacement to historical triggering factors is not uniform but exhibits a pronounced non-stationary memory effect (Ju et al., 2025; Chen et al., 2023). On the one hand, recent rainfall and reservoir water level changes usually have a more direct impact on current deformation. On the other hand, the influence of certain historical events may not manifest until several months later (Lustberg et al., 2023). For example, the rise in groundwater level caused by continuous heavy rainfall during the rainy season takes time to propagate to the slip zone, thereby inducing step-like displacement growth. Furthermore, although the rapid drawdown period of the reservoir water level lasts only a few weeks, the resulting disturbance to the seepage field may continue to drive deformation at the front edge of the landslide for several months thereafter (Chen et al., 2021). Therefore, how to enable the prediction model to automatically identify which historical periods carry “more important” information has become a key issue for improving the accuracy of landslide displacement prediction.

To address this, a temporal attention mechanism is introduced on top of the LSTM sequence encoding layer. This mechanism acts as a “historical information filter”: for each prediction time step t, the model evaluates the importance of the hidden states at each of the past T time steps (T = 12 months in this paper) and accordingly assigns different attention weights to different historical time steps. The complete computational process of the temporal attention mechanism is as follows:

Let the hidden state output by the LSTM network at historical time step be , where is the number of LSTM units. First, each is fed into a single-layer fully connected network to compute the unnormalized attention score at that time step (Equation 8):where , and are learnable parameters. Then, the Softmax function is applied to the scores of all historical time steps to obtain the normalized temporal attention weights (Equation 9): is a scalar between 0 and 1, representing the contribution ratio of the τ-th historical time step to the current prediction, with the sum of the weights across all time steps equal to 1. Finally, the hidden states from each historical time step are weighted and summed according to these weights to obtain the fused temporal feature vector (Equation 10):

The temporal attention mechanism provides the model with the ability to adaptively adjust the “memory length” and “memory focus” based on the data. For the Baishuihe landslide, its deformation exhibits pronounced seasonal acceleration characteristics. The main period of displacement step-like occurrence is from May to September each year, and this acceleration process is often driven jointly by the rainfall of the current rainy season and the cumulative effect of preceding reservoir water level drawdown.

2.4 Loss function and regularization strategy

Landslide displacement prediction is essentially a regression task. In this paper, the Mean Squared Error (MSE) is adopted as the primary loss function, which takes the following form (Equation 11):where and are the actual cumulative displacement and the predicted cumulative displacement of the -th monitoring point at time , respectively, and is the number of time steps in the training set. MSE penalizes large errors quadratically, forcing the model to prioritize reducing predictions with substantial deviations (Pak et al., 2025). In practical applications, underestimation of landslide displacement may lead to early warning failure, so this “conservative” bias is beneficial. However, a potential issue with using MSE alone is that the model may focus excessively on monitoring points with large displacement magnitudes while relatively neglecting those with smaller displacements (e.g., front-edge points), because the squared error of the latter accounts for a smaller proportion of the total loss (Fan et al., 2022; Wang Q. et al., 2022). To balance the contribution of each monitoring point to the loss function, a monitoring point weighting strategy is introduced: each monitoring point is assigned a weight inversely proportional to its measured displacement magnitude:

, where

The weighted loss function is Equation 12:

Furthermore, to prevent the model from overfitting (especially given the large number of learnable parameters in the graph convolution and attention layers), an L2 regularization term is added to the loss function (Equation 13):where denotes the set of all trainable parameters (excluding bias terms), and λ is the regularization coefficient (in this paper, ). The inclusion of the regularization term encourages the model to favor solutions with smaller parameter values, thereby reducing the model’s sensitivity to random noise in the training data.

2.5 Model architecture selection

To thoroughly evaluate the performance of GSTA-Net, it is necessary to compare it with existing graph spatio-temporal modeling frameworks. In this paper, we select DCRNN (Diffusion Convolutional Recurrent Neural Network) as the primary baseline model for the following reasons.

First, DCRNN is a state-of-the-art model that has been validated in the existing literature on landslide displacement prediction. Second, the diffusion convolution mechanism of DCRNN is highly consistent with the geological context of landslide deformation propagation. DCRNN models the propagation of information on a graph as a diffusion process of a k-step random walk, and its directed graph structure can capture the unidirectional deformation transfer of “rear-edge tension → front-edge push”. This characteristic makes it a suitable benchmark for assessing the competitiveness of GSTA-Net in landslide monitoring scenarios with a small number of nodes.

3 Study area and data

The Baishuihe landslide is located in Zigui County, Hubei Province, within the Three Gorges Reservoir area, on the left bank of the Qinggan River, a tributary of the Yangtze River, approximately 56 km from the Three Gorges Dam (Lu et al., 2024; Miao et al., 2021). Its geographic coordinates are approximately 110°37′–110°38′ E and 30°57′–30°58′ N. The main sliding direction of the landslide is approximately SE 150°. The planar shape of the sliding mass is an irregular tongue, with a longitudinal length of about 600 m and a transverse width of about 300 m, covering a total area of approximately 1.8 × 10⁵ m², as shown in Figure 2.

FIGURE 2

The sliding mass has an average thickness of approximately 30 m and a total volume of about 5.4 × 10⁶ m³, classifying it as a medium-sized soil landslide. The landslide mass is primarily composed of Quaternary colluvial and ancient landslide deposits, with lithology of block-stone soil mixed with silty clay, exhibiting a loose to moderately dense structure. The block-stone content ranges from 50% to 65%, with particle sizes predominantly between 5 and 20 cm, and the main components of the blocks are sandstone and mudstone (Jiang et al., 2021). The slip zone soil is gravelly silty clay, with a thickness of 0.5–2.0 m, exhibiting a plastic to hard-plastic state. The sliding bed consists of interbedded sandstone and mudstone of the Lower Jurassic Xiangxi Formation (), with rock stratum attitude of 120∘∠15∘, intersecting the main sliding direction at a small angle. The front edge of the landslide is at an elevation of approximately 135 m (below the normal reservoir water level of the Three Gorges Reservoir, 175 m), and the rear edge is at an elevation of approximately 320 m, with an average slope of about 25°. The front edge directly faces the water, being submerged when the reservoir water level rises and exposed when it falls. This topographical condition subjects the front edge to prolonged fluctuations of the reservoir water level, making it an important trigger window for landslide deformation, as shown in Figure 3.

FIGURE 3

3.1 Monitoring network and displacement data

To track the deformation dynamics of the Baishuihe landslide, relevant authorities established a GPS displacement monitoring network on the landslide mass in 2007. The monitoring points are distributed along the main sliding axis and transverse profiles, totaling 11 GPS monitoring points. Figure 4 shows the planar distribution of the monitoring points on the landslide mass. Because monitoring points ZG091, ZG092, ZG094, ZG119, and ZG120 are located outside the early warning zone and exhibit very small displacements, while monitoring point ZG118 is situated in the central part of the landslide and can reflect the entire evolution process of displacement and its monitoring data are relatively complete, facilitating data-driven modeling this paper mainly adopts the monitoring data from point ZG118 to validate the feasibility and effectiveness of the proposed method. The spatial attention analysis involves six monitoring points within the warning line: ZG118, ZG093, XD-01, XD-02, XD-03, and XD-04. The statistical characteristics of the cumulative displacement for each monitoring point are shown in Table 1.

FIGURE 4

Data preprocessing and missing value handling: In the original displacement records, monitoring point ZG118 had 1 day of missing data in August 2007 and 1 day in March 2008 (each caused by temporary GPS signal interruptions). These missing values were filled using linear interpolation. The remaining five monitoring points had complete data with no missing values. The displacement time series for all monitoring points were resampled to a monthly frequency (taking the cumulative displacement value on the last day of each month) to align with the monthly scale of the rainfall and reservoir water level data.

Spatial distribution characteristics of displacement: As shown in Table 1, the cumulative displacements at ZG118 and ZG093 are significantly larger than those at the front and middle monitoring points, with maximum cumulative displacements reaching 312.6 mm and 298.4 mm, respectively, while the maximum displacement at XD-01 is only 86.3 mm. This pattern is consistent with the “progressive retrogressive failure” mode: the displacement is largest in the rear-edge tension zone and relatively smaller in the front-edge resistance zone. Such spatial gradient information constitutes an important learning target for the spatial attention mechanism.

Data splitting: The monthly dataset from December 2006 to December 2012 was chronologically divided into three parts: training set (December 2006 – December 2009, 37 monthly samples), validation set (January 2010 – December 2011, 24 months), and test set (January 2012 – December 2012, 12 months). The training set is used for model parameter learning, the validation set is used for hyperparameter tuning and early stopping, and the test set is used only for final performance evaluation without participating in any training process.

3.2 Rainfall and reservoir water level data

The performance of landslide displacement prediction models heavily depends on the quality and representativeness of the input external triggering factors. For the Baishuihe landslide, rainfall and reservoir water level fluctuations are the two main environmental variables driving its step-like deformation. However, their effects on displacement are not simply linear and additive but exhibit complex time-varying sensitivity, lag effects, and interactions. Therefore, when constructing model input features, it is insufficient to merely feed raw data directly into the network; a deep understanding of the temporal dynamics of these two factors and their physical relationships with displacement is required. This section details the data sources, statistical characteristics, and temporal response relationships of rainfall and reservoir water level in relation to landslide displacement, providing a foundation for the subsequent design of the factor attention mechanism.

3.2.1 Rainfall characteristics

The area where the Baishuihe landslide is located belongs to a subtropical monsoon humid climate zone, with abundant rainfall but extremely uneven seasonal distribution. The rainfall data used in this paper were obtained from a dedicated meteorological station (Station No. 57583) in the Three Gorges Reservoir area, provided by the China Meteorological Data Service Center (Liu et al., 2024). This station is located approximately 4.2 km northeast of the landslide mass at an elevation of 210 m, and its observational records can reasonably reflect the rainfall conditions of the landslide. Daily rainfall data from December 2006 to December 2012 were obtained from this station, with a temporal resolution of 1 day. To align with the monthly frequency of displacement monitoring, the daily rainfall was aggregated into monthly cumulative rainfall (unit: mm). The maximum daily rainfall within a month and the number of rainy days within a month were also calculated as candidate features, as shown in Figure 5. It is worth noting that nearly all displacement steps of the Baishuihe landslide occur during the rainy season or within 1–2 months after the rainy season ends. This phenomenon has been reported in previous studies but usually lacks a quantitative description of the lag magnitude.

FIGURE 5

The mechanism by which rainfall affects landslide deformation is mainly reflected in two aspects: first, rainwater infiltration increases the self-weight of the sliding mass, thereby increasing the driving force; second, infiltrating water softens the slip zone soil, reducing its shear strength parameters (especially cohesion). However, neither of these processes is instantaneous. It often takes days to weeks from the occurrence of rainfall to a significant rise in pore water pressure within the slip zone. This lag effect implies that when predicting displacement for a given month, one cannot rely solely on the rainfall of that month; the cumulative rainfall over previous months or the rainfall pattern within a specific time window must also be considered. Although traditional LSTM models are capable of remembering historical information, they treat all historical time steps equally (or only implicitly decay information through gating mechanisms), lacking selective focus on critical lag periods. This is precisely why the temporal attention mechanism is introduced in this paper, allowing the model to automatically learn the “effective lag window” of rainfall influence. In addition, the intensity distribution of rainfall is also important: a prolonged low-intensity rainfall and a short-duration heavy rainstorm may produce different infiltration effects. Although this paper uses monthly cumulative rainfall as input (losing daily distribution information), finer-grained rainfall intensity features can be incorporated in future work. Through the factor attention mechanism, the current model can dynamically adjust the weight assigned to the rainfall factor. For example, when the first heavy rainfall occurs after a prolonged dry spell, the model may assign a higher weight to the rainfall factor, because the sliding mass is then characterized by well-developed fissures and strong infiltration capacity, making the deformation response more sensitive.

3.2.2 Reservoir water level operation pattern

Since the Three Gorges Reservoir began impoundment in 2003, a well-defined “storing clear water and discharging turbid water” regulation model has been established (Zhao et al., 2021). The reservoir water level data used in this paper were obtained from the publicly released “Daily Report of Three Gorges Reservoir Operation Water Levels” by China Three Gorges Corporation (http://www.ctg.com.cn). Daily water level records (unit: m) from December 2006 to December 2012 were extracted, as shown in Figure 6. From these data, three candidate features were constructed: monthly average reservoir water level, maximum daily drawdown rate within the month (unit: m/d), and maximum daily rise rate within the month. Correlation analysis with the displacement data revealed that the monthly average reservoir water level and the maximum monthly drawdown rate exhibited the strongest predictive power for displacement (partial correlation coefficients of −0.48 and 0.56, respectively), while the rise rate showed no significant correlation with displacement (p > 0.1). Therefore, the final input factors of the model include the monthly average reservoir water level and the maximum monthly drawdown rate, while the rise rate is excluded.

FIGURE 6

The mechanism by which reservoir water level affects landslide deformation is entirely different from that of rainfall. When the reservoir water level drops rapidly, the buoyancy force at the front edge of the landslide decreases sharply, which effectively increases the self-weight of the sliding mass. At the same time, the hydraulic gradient of outward seepage within the slope increases, generating a seepage force directed out of the slope. Both effects reduce landslide stability and induce accelerated deformation of the front edge and even the entire sliding mass. Moreover, the influence of reservoir water level drawdown exhibits virtually no lag (or only a very short lag, typically on the order of days), because changes in the seepage field are transmitted almost instantaneously to the slip zone near the front edge. In contrast, during the high-water operation period, although the water pressure is high, the buoyancy force is also large, which actually favors stability. However, prolonged immersion may soften the rock and soil at the front edge, representing a slow cumulative effect. The reservoir water level drawdown rate should be regarded as a high-priority, short-lag triggering factor, and the model should assign high weights to recent drawdown rates when making predictions. Conventional time series models treat the reservoir drawdown signal equally with other factors, whereas the factor attention mechanism in this paper dynamically allows the model to automatically increase the weight of the drawdown rate during January–June and decrease it during other months, which is an effective embedding of physical prior knowledge.

4 Results and analysis

4.1 Prediction results and accuracy evaluation

A unified data split was adopted: the training set from December 2006 to December 2009 (37 monthly samples), the validation set from January 2010 to December 2011 (24 months), and the test set from January 2012 to December 2012 (12 months). Based on this split, the GSTA-Net model was trained and tested. Figure 7 shows a comparison between the predicted cumulative displacement and the measured values at monitoring point ZG118 using GSTA-Net.

FIGURE 7

Three metrics were used for quantitative evaluation: root mean square error (RMSE), mean absolute percentage error (MAPE), and coefficient of determination (R²). The single-point prediction errors of GSTA-Net on the test set for monitoring point ZG118 are shown in Table 3 (to maintain consistency with subsequent multi-model comparisons, these results have been summarized in Table 3). The RMSE is 11.38 mm, the MAPE is 4.52%, and R² is 0.964. It should be noted that all quantitative evaluations in this paper are based on monitoring point ZG118; the values in the table represent the prediction errors for this single point, rather than an average across multiple points.

Multi-model comparison: To validate the superiority of GSTA-Net, four baseline models were selected for comparison: GWO-SVM (support vector machine optimized by Grey Wolf Optimizer, single-point modeling), CNN-LSTM (CNN for spatial feature extraction, requiring interpolation of monitoring points onto a regular grid, no attention mechanism), 1D-CNN-LSTM (CNN kernel size set to 1, unable to extract spatial correlations, degenerating into a temporal model), and LSTM-Attention (temporal attention only, no spatial module, single-point modeling). All models were trained and tested under the same data split. The prediction errors for cumulative displacement at monitoring point ZG118 on the test set for each model are summarized in Table 3, the predicted displacement curves are compared in Figure 8, and the bar charts of RMSE and MAPE are shown in Figure 9.

FIGURE 8

FIGURE 9

From Table 3 and Figure 9, it can be observed that:

GSTA-Net achieves an RMSE of 11.38 mm, a MAPE of 4.52%, and an R² of 0.964, outperforming all baseline models.

Compared with CNN-LSTM (RMSE = 12.87 mm), GSTA-Net reduces RMSE by 11.6% and MAPE by 11.2%.

Compared with GWO-SVM (RMSE = 14.46 mm), GSTA-Net reduces RMSE by 21.3% and MAPE by 33.8%.

CNN-LSTM outperforms 1D-CNN-LSTM (RMSE = 13.52 mm), indicating that spatial feature extraction on regular grids still provides some benefit. GSTA-Net further outperforms CNN-LSTM, demonstrating that graph convolution for irregular spatial structures is more effective than regular grid interpolation.

LSTM-Attention (RMSE = 12.35 mm) outperforms GWO-SVM but still underperforms relative to GSTA-Net, suggesting that temporal attention alone can improve prediction accuracy, but the combination with spatial graph convolution and factor attention yields even better performance.

In addition, the training time (200 epochs per single run) for each model was recorded. GSTA-Net took approximately 9.2 s, CNN-LSTM took 7.1 s, and although GWO-SVM was fast for single-point training (4.5 s per point), it required separate optimization for each point, resulting in a total time of 27 s (for 6 points). GSTA-Net achieves the best accuracy with acceptable training cost.

4.2 Cross-validation and training scale sensitivity analysis

The training set used in this study contains only 37 monthly time steps (December 2006 to December 2009), which is relatively limited. To verify whether the attention weights learned by GSTA-Net are statistically stable rather than random noise, we supplement this section with two analyses: time-series expanding-window cross-validation and training scale sensitivity analysis.

4.2.1 Expanding-window cross-validation

The data from December 2006 to December 2011 were chronologically divided into five folds. For each fold, the training set spans from the start time to a certain cutoff year, and the validation set is the next complete hydrological year (January–December). The test set (2012) remains unchanged for final evaluation. The results are shown in Table 4.

From Table 4 it can be seen that: ① Even with only 13 months of training data (Fold 1), the model still converges and achieves a validation RMSE of 12.21 mm, which is only 7.3% higher than that of the full model (11.38 mm). ② As the training data increase, the validation error decreases monotonically without overfitting. ③ The average RMSE across the five folds is 11.73 mm, with a standard deviation of only 0.34 mm, indicating that the model is insensitive to the choice of training set start and end times.

4.2.2 Training scale sensitivity analysis

To further assess the impact of training set size, different proportions of the training data (40%, 60%, 80%) were randomly subsampled. Models were trained on each subsample, and both the test set RMSE and the stability of the spatial attention weights were recorded. The stability of the attention weights was evaluated using Kendall’s τ rank correlation coefficient, with the weight ranks from the model trained on 100% of the data taken as the reference. Each proportion was repeated 10 times. The results are shown in Table 5.

Table 5 shows that: ① Even when the training data are reduced to 22 months (60%), the model still maintains high accuracy (RMSE 12.08 mm) and the attention ranks are highly consistent with those of the full model (τ = 0.89). ② Even with only 15 months of data (40%), the consistency of the attention ranks remains strong (τ = 0.83), although the prediction error increases notably. This indicates that the attention patterns learned by GSTA-Net remain stable even when the training sample size is reduced to about 20 months and do not degenerate into random distributions.

4.2.3 Physical consistency as intrinsic validation

In addition to the above quantitative analyses, the strong agreement between the attention weights output by the model and the known deformation mechanisms of the Baishuihe landslide further demonstrates that the model has learned meaningful physical patterns: the spatial attention concentrates on the rear-edge tension zone, the factor attention exhibits seasonal alternation, and the temporal attention peaks appear with a lag of 1–2 months. If the attention weights were dominated by random noise, the probability that they would simultaneously conform to all three physical priors is virtually zero. Therefore, despite the limited amount of training data, the spatiotemporal patterns revealed by the model have a reliable scientific basis.

4.3 Visualization and interpretability analysis of attention weights

The core value of the attention mechanism lies not only in improving prediction accuracy but also in the fact that the output weight vectors can serve as a “transparent window” into the model’s decision-making process. In this section, we present the attention distributions learned by GSTA-Net from three perspectives—spatial, factor, and temporal—and explain how each distribution corroborates the actual deformation mechanisms of the Baishuihe landslide.

4.3.1 Spatial attention: identification of key monitoring areas

To quantify the contribution of different monitoring points to the overall displacement prediction, a “node-masking sensitivity analysis” was conducted. After model training was completed and all parameters were fixed, the input features of each monitoring point were sequentially set to zero, and the model’s RMSE on the entire test set was recalculated. The larger the increase in RMSE (ΔRMSE) caused by masking a given monitoring point, the more critical the spatial information provided by that point is for prediction. The ΔRMSE values were normalized to the [0, 1] interval to obtain the spatial attention score for each monitoring point.

FIGURE 10

The spatial attention distribution directly answers the engineering question: “Which parts of the landslide deserve the most attention?” Based solely on empirical judgment, engineers might consider the front edge (directly affected by reservoir water) to be the most important, but the model results suggest that the rear edge is the “information-rich zone.” This data-driven conclusion can help optimize monitoring network layout and explain why certain monitoring points, despite exhibiting small displacements, carry high weight for early warning.

4.3.2 Factor attention: dynamically tracking the dominant triggering factors of the landslide

The factor attention weights are computed by the formula presented earlier, indicating the degree of attention paid by the model to the -th input factor (monthly rainfall, monthly average reservoir water level, reservoir water level drawdown rate) at prediction time . We extracted the factor weights for each month across the entire test set and plotted them as a stacked area chart (Figure 11). To reduce random fluctuations, a 3-month moving average was applied.

FIGURE 11

Figure 11 clearly shows the seasonal periodic alternation of the dominant factors:

Winter to early spring (January–March): The weight of the reservoir water level drawdown rate dominates. During this period, the Three Gorges Reservoir begins discharging from 175 m to 145 m, with the drawdown rate reaching its annual peak. The model correctly assigns the highest weight to this factor, as the reservoir drawdown is the sole strong driving force under low-rainfall conditions.

Late spring to early summer (April–June): The rainfall weight rises rapidly, while the reservoir drawdown rate weight declines slowly. This stage is a transition period where the two factors exhibit a trade-off, and the model demonstrates keen sensitivity to this “two-factor coupling.”

Midsummer rainy season (July–September): The rainfall weight reaches its annual peak, becoming the absolutely dominant factor. During this period, the reservoir water level has stabilized at the low level of 145 m, the drawdown rate approaches zero, and its weight drops to 0.15–0.20. Notably, although the absolute elevation of the reservoir water level still exists, the model largely ignores this information.

Autumn (October–December): The reservoir begins impounding, the water level rises, and the rainy season ends. The model assigns some weight to rainfall, but shifts more weight to the reservoir water level. Although a rising reservoir water level favors slope stability, the weights output by the model represent only “attention” rather than the direction (positive or negative) of influence. This phenomenon will be discussed in Section 5.1.

The time-varying pattern of factor attention provides a “dynamic threshold” approach for early warning systems: during the reservoir drawdown period, monitoring should focus primarily on the drawdown rate, with an early warning triggered when the drawdown rate exceeds 0.6 m/d; during the rainy season, cumulative rainfall should serve as the main indicator. Furthermore, interannual comparisons of factor weights may reveal whether the landslide’s sensitivity to external conditions has changed.

4.3.3 Temporal attention: quantifying the memory length and lag effects of landslide deformation

The temporal attention weights indicate the degree to which the model relies on the LSTM hidden state at the τ-th historical time step when predicting the current displacement. We aggregated the weights from all 12 prediction time steps in the test set and averaged them according to the lag month (where −1 represents the previous month, −2 represents 2 months prior, and so on), obtaining an average temporal attention distribution curve (Figure 12). To test the statistical significance of the weights, 100 Bootstrap resampling iterations were performed, and the 95% confidence intervals were plotted.

FIGURE 12

As shown in Figure 12, the weights for lags of 1 and 2 months are significantly higher than those for other lags (mean values of 0.29 and 0.25, respectively, with non-overlapping confidence intervals). This indicates that the model relies primarily on the historical states of the most recent 2 months to predict the displacement in the following month. This finding is consistent with the physical inertia of landslide deformation: the deformation rate of the previous month tends to persist into the next month, and the effect of reservoir water level drawdown is strongly felt within a lag of 1–2 months.

The weights for lags of 3 and 4 months remain non-negligible (approximately 0.14 and 0.11, respectively) and are significantly higher than those for longer lags. This window corresponds to the lag effect of rainfall infiltration: heavy rainfall in the middle of the rainy season requires 2–3 months to sufficiently raise the pore water pressure in the slip zone and induce significant displacement.

Weights for lags of 5 months or more are all below 0.06, and their confidence intervals include zero, indicating that historical information beyond half a year contributes little to the current prediction. This suggests that the geological memory length of the Baishuihe landslide is approximately 4–5 months, with earlier deformation events effectively “forgotten.”

The distribution of temporal attention directly answers the question: “How far back should historical data be considered?” For the Baishuihe landslide, using an input window longer than 5 months yields no additional benefit and may instead introduce noise. This finding can be used to simplify the model: reducing the LSTM time step from 12 months to 4–5 months reduces computational cost while maintaining accuracy. Furthermore, the weight peak at a lag of 3–4 months provides a quantitative basis for early warning of rainfall-induced displacement: following heavy rainfall, a monitoring attention period of 3–4 months should be sustained.

4.4 Ablation experiments

To systematically evaluate the respective contributions of the three core modules in GSTA-Net (graph convolution spatial module, temporal attention, and factor attention), a series of ablation experiments were designed. For each variant model, only one module was removed while all other structures and hyperparameters remained unchanged, and the models were retrained and retested under identical data partitions. Each experiment was repeated five times to eliminate the effect of random initialization, and the average RMSE and MAPE are reported.

4.4.1 Description of variant models

GSTA-Net (Full): Serves as the baseline. Includes the graph convolution spatial module, temporal attention, and factor attention.

w/o Spatial: Removes the graph convolution layer and replaces the spatial module with a simple fully connected layer that independently transforms the raw features of each monitoring point (without introducing information exchange between nodes). The model still takes data from multiple monitoring points as input, but there is no spatial feature fusion among points.

w/o Temporal Att: Removes the temporal attention mechanism. The LSTM output directly uses the hidden state of the last time step (instead of the weighted sum ). Factor attention and the spatial module are retained.

w/o Factor Att: Removes the factor attention mechanism. External triggering factors are fed directly into the LSTM (without dynamic factor-level weighting). Temporal attention and the spatial module are retained.

w/o Both Att: Removes both temporal attention and factor attention, retaining only the spatial module + vanilla LSTM.

4.4.2 Quantitative analysis of the contribution of each module

4.4.3 Quantitative comparison with DCRNN

To further evaluate the competitiveness of GSTA-Net in the field of graph spatio-temporal learning, we implemented DCRNN (Diffusion Convolutional Recurrent Neural Network) and conducted a quantitative comparison under identical experimental settings. DCRNN employs diffusion convolution and a Seq2Seq architecture, modeling information propagation on a graph as a k-step random walk diffusion process, and incorporates teacher forcing to mitigate error propagation in long-sequence prediction. The two models share the same data split, input features, and graph adjacency matrix. For a fair comparison, the input window length of DCRNN was set to months, the prediction window to months, the number of diffusion steps K = 2, the hidden layer dimension to 64, the batch size to 8, and the learning rate to 0.001. The test set results are shown in Table 6.

The experimental results show that GSTA-Net achieves better prediction accuracy than DCRNN, with an RMSE reduction of 0.67 mm. This advantage can be attributed to the following two points (Table 7).

First, the factor attention mechanism of GSTA-Net explicitly models the dynamic weights of external triggering factors, enabling it to capture the alternation of dominant factors across different hydrological stages. In contrast, DCRNN incorporates external factors only as part of the node features into the encoder and cannot distinguish the dynamic contributions of different factors. For step-like deformation scenarios such as the Baishuihe landslide, where rainfall and reservoir water level alternately dominate, the targeted design of factor attention is crucial.

Second, GSTA-Net adaptively filters historical information through its temporal attention mechanism, identifying a 1–2 months window as the main memory period on the test set. Although DCRNN propagates spatial information via diffusion convolution, its GRU architecture lacks an explicit selective focusing mechanism for processing historical temporal information. Furthermore, the spatial, factor, and temporal attention weights output by GSTA-Net provide multi-dimensional interpretability that DCRNN does not offer, which holds engineering value for geological disaster warning and decision-making. The code and data split for GSTA-Net presented in this paper have been made publicly available to facilitate fair benchmarking.

4.4.4 Trade-off between computational complexity and accuracy gain

The synergistic effect between temporal attention and factor attention is primarily additive rather than strongly positive synergistic. Here we further analyze whether the increase in computational cost introduced by each attention mechanism individually and by their combination is justified by the corresponding improvement in accuracy. Under the model configuration used in this paper, the single-training time and test set RMSE for each model variant are shown in Table 8.

In summary, although temporal attention and factor attention do not exhibit a strong synergistic effect, each independently contributes significantly. The additional computational cost introduced by jointly incorporating both modules is justified by the practical improvement in prediction accuracy and the extra physical interpretability benefits. In high-stakes decision-making scenarios such as landslide early warning, even modest improvements in accuracy and mechanism transparency are of non-negligible value.

5 Discussion

5.1 Model advantages and physical consistency

The proposed GSTA-Net model outperforms traditional methods in both prediction accuracy and interpretability. Its advantages are primarily reflected in three aspects:

First, effective modeling of irregular spatial structures. Through the graph convolutional network, the model can directly leverage the original spatial topology of monitoring points, avoiding the regular grid interpolation required by CNNs and the associated information distortion. Node-dropping sensitivity analysis shows that the model correctly identifies the rear edge as the critical deformation zone, which is consistent with the “progressive retrogressive failure” mechanism of the Baishuihe landslide. This capability allows GSTA-Net to be generalized to landslides with arbitrary monitoring layouts without needing to redesign the spatial feature extraction method.

Second, physical interpretability of dynamic factor weights. The temporal variation curves of the factor attention weights correspond precisely to the dominant factors in different phases of the hydrologic year: reservoir water level dominates during the drawdown period, rainfall dominates during the rainy season, and neither is significant during the high-water period. This consistency provides additional credibility to the model’s prediction results. In practical early warning, when the factor attention indicates abnormally high rainfall weights, vigilance should be exercised regarding cumulative effects even if the current forecasted rainfall is modest; conversely, if the reservoir drawdown rate weight remains persistently high, monitoring of the front edge should be intensified.

Third, automatic quantification of lag effects. The distribution of temporal attention weights reveals that the optimal memory length for the Baishuihe landslide is 3–4 months, with information from the most recent 1–2 months being the most important. This value can be used to simplify subsequent models (e.g., a fixed-window LSTM without attention could be applied directly, albeit with some loss of accuracy) and can also serve as a reference for designing monitoring frequencies for other landslides in the same region.

5.2 Model limitations

The monitoring data used in this paper are limited to the period 2006–2012 and do not include observations from the past decade, which may affect the robustness assessment of the model under current reservoir water level operation conditions. Data timeliness is one of the main limitations of this study. It should be noted that displacement monitoring of the Baishuihe landslide has been ongoing continuously since the impoundment of the Three Gorges Reservoir in 2003. The reasons why we did not extend the data range (to include 2018 or even 2020) are primarily due to restricted access to data and missing data at some monitoring points in later years. To address this limitation, we plan to incorporate monitoring data from 2013 to 2020 in future work to validate the model’s generalizability over a longer time span and to examine the impact of reservoir group joint operation practices on landslide deformation patterns. It is worth noting that the “storing clear water and discharging turbid water” operation mode of the Three Gorges Reservoir has been essentially established since impoundment in 2003. The period 2006–2012 already covers a complete operation cycle, including the reservoir water level drawdown period → low-water period → rising period → high-water period. The reservoir water level variation pattern during 2006–2012 (slow release from 175 m to 145 m in winter and early spring, operation at 145 m in summer, and refilling to 175 m in autumn) is essentially consistent with that of subsequent years (e.g., 2013–2020). Therefore, the factor-displacement mapping learned by the model from the 2006–2012 data remains representative for later years.

It is also noteworthy that the Transformer architecture has achieved significant progress in remote-sensing landslide identification in recent years. A series of works such as DBSANet, Lights-Transformer, and D²FLS-Net have fully demonstrated the advantages of Transformer in static landslide image segmentation. The dual-attention mechanism adopted in our model focuses on dynamic weight allocation for multi-point spatial correlations and multi-factor temporal contributions, which differs in functional positioning from the multi-head self-attention in the aforementioned methods (which focuses on global contextual relationship modeling and pixel-level feature interaction). How to fuse these two attention paradigms within a unified framework to construct a landslide prediction model that possesses both spatial topology modeling capability and global dependency capturing ability is an important direction for future research. Furthermore, cross-modal fusion of multi-modal remote sensing data (e.g., optical imagery, InSAR deformation fields, DEM) with ground-based monitoring time-series data may provide richer information sources for landslide displacement prediction. Going further, for the yet-to-be-explored direction of applying Transformer/hybrid attention to time-series prediction of landslide displacement, one could consider using time-series Transformers (e.g., Informer, Autoformer) or deeply fused architectures of Transformers and graph neural networks, extending them within the framework of our GSTA-Net.

5.3 Comparison and integration prospects of interpretability methods

In this paper, attention weights are used as the primary tool for model interpretability, outputting attention distributions across three dimensions: spatial, factor, and temporal. Compared with methods such as SHAP, the advantage of the attention mechanism lies in the fact that its weights are learned end-to-end within the model, jointly optimized with the prediction target, and thus reflect the model’s actual focus during decision-making rather than serving as post hoc explanations. Moreover, attention weights are inherently visualizable, can be directly mapped to heatmaps or time-varying curves, and are convenient for engineers to intuitively understand the model’s reasoning. However, the interpretability of attention mechanisms also has clear limitations. First, attention weights measure the model’s “level of focus” on input information but do not directly quantify the magnitude and direction of each input factor’s marginal contribution to the output value. Therefore, they cannot answer quantitative attribution questions such as “for each 1 mm increase in rainfall, by how much will the displacement increase?” In contrast, SHAP, by computing Shapley values for features, can provide specific contribution values of each factor to the prediction result and can offer explanations at both global and local scales. Second, the attention mechanism lacks physical constraints. Although the weights learned by the model are consistent with the landslide deformation mechanisms, they do not explicitly embed mechanical equations such as slope seepage or effective stress changes, and thus cannot guarantee physical consistency under all prediction scenarios. Meanwhile, the PINN approach, by incorporating partial differential equations (e.g., Richards’ seepage equation, Newmark displacement equation) as residual terms into the loss function, can enforce that the model outputs satisfy fundamental physical laws such as mass conservation and momentum conservation. The fundamental difference between our model and the aforementioned methods is: the attention mechanism answers “what does the model focus on?”, SHAP answers “how much does each factor contribute?”, and PINN answers “does the prediction comply with physical laws?” The three are not substitutes for one another but are complementary. In high-stakes decision-making scenarios such as landslide prediction, a single interpretability method may not be sufficient to meet all requirements. Therefore, future work can proceed in the following directions. First, combine attention weight visualization with SHAP analysis to obtain, in the spatial, factor, and temporal dimensions, both weight distributions and quantitative comparisons of marginal contributions. Second, drawing on the idea of PINNs, introduce simplified physical constraints into the loss function of GSTA-Net (e.g., constraining the trend of pore water pressure and displacement via mass conservation), thereby organically integrating data-driven attention learning with embedded physical laws to build a prediction model with greater mechanical consistency.

6 Conclusion

In summary, by organically integrating a graph convolutional network with a dual-attention mechanism, GSTA-Net has achieved substantial progress in irregular spatial structure modeling and model interpretability. The model not only enables high-precision multi-point displacement prediction but also reveals the spatiotemporal mechanisms of landslide deformation through attention weight visualization, providing a new technical approach for intelligent early warning and monitoring network optimization of reservoir landslides.

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