Abstract
Landslides often exhibit step-like deformation and abrupt displacement increases, making accurate early warning highly challenging. Understanding the evolutionary mechanisms and extracting effective predictive features from dynamic environmental factors are critical for improving forecasting performance. This study proposes a hybrid forecasting model based on a deep understanding of landslide evolution mechanisms. First, Variational Mode Decomposition (VMD) was employed to analyze the dynamic response relationship between displacement and influencing factors (e.g., rainfall and reservoir water level). Then, Double Exponential Smoothing (DES) was applied to decompose cumulative displacement into trend and periodic components, enabling the identification of effective external input features. Finally, the Informer model, integrated with a multi-head attention mechanism and pooling layers, was developed to capture critical periodic information from time-series data. The proposed model was validated using six consecutive years of monitoring data from the Baishuihe Landslide in the Three Gorges Reservoir Area. The results show that the model achieves high prediction accuracy, significantly outperforming mainstream machine learning models with superior error control.
1 Introduction
The frequent occurrence and severe hazards of landslides have made intelligent early warning an urgent need in current geological disaster prevention and mitigation (Strząbała et al., 2024; Lin et al., 2025). This demand is particularly prominent in the Three Gorges Reservoir Area, where complex geological conditions, combined with periodic water level fluctuations and heavy rainfall, make it highly prone to landslides. Numerous landslide masses remain active in the area to this day (Wang et al., 2021). In response to these challenges, the increasing sophistication of modern surveying technologies has made it essential to automate the processing of monitoring data using deep learning and machine learning techniques, thereby developing efficient intelligent prediction models (Ahmed et al., 2023).
The core challenge in landslide displacement prediction lies in accurately estimating the periodic component, particularly during rapid deformation phases (Zhang Y. G. et al., 2021). Current prediction methods commonly adopt an additive model framework, which involves decomposing time-series displacement into trend and periodic components using techniques such as moving average, HP filter, EEMD, and VMD, before modeling them separately (Shao et al., 2024; Yang et al., 2024; Wang et al., 2025). The trend component, governed by inherent geological conditions, changes gradually and is relatively easy to predict. In contrast, the periodic component, influenced by external factors, exhibits complex dynamics, and its nonlinear fluctuations are the primary cause of prediction difficulties (Zhang et al., 2022). The methodological framework for landslide displacement prediction mainly includes deterministic physical models, statistical models, and nonlinear models (Wang et al., 2022). In recent years, with advances in machine learning and artificial intelligence, nonlinear models have become essential tools for addressing periodic displacement prediction in landslides. A range of algorithms such as Support Vector Machine (SVM), Extreme Learning Machine (ELM), Gated Recurrent Unit (GRU), and Long Short-Term Memory (LSTM) have been widely applied (Zhang et al., 2022; Pei et al., 2021; Wang et al., 2025). However, given the distinct performance characteristics of different algorithms, making appropriate choices in practical applications is crucial. Establishing an efficient and reliable landslide displacement prediction model requires, first and foremost, an in-depth study of the landslide deformation response mechanism under the coupled influence of reservoir water levels and rainfall. This involves identifying key influencing factors and analyzing the lag effects of displacement in response to these factors, based on a clear understanding of the physical significance of each displacement component (Qu et al., 2025). This need is particularly pronounced in the Three Gorges Reservoir Area, where landslide reactivation and deformation are significantly influenced by periodic reservoir water level fluctuations and rainfall during the flood season (Hou et al., 2022). To address the challenge of large prediction errors in periodic displacement, the Informer model, known for its excellent performance in long-sequence forecasting, can be introduced. Built on an improved self-attention mechanism and an integrated convolutional network, the Informer efficiently captures key local features without information loss. With its high accuracy and computational efficiency, it holds great potential for achieving accurate early warning and prediction of landslides.
In recent years, the framework for landslide displacement prediction has progressively shifted from traditional physical and statistical models toward intelligent, data-driven approaches. In international research, Lan et al. (2022) developed an early warning system based on remote sensing technology for identifying landslide precursors; Wang J. et al. (2023) revealed the deformation mechanism of earthquake-induced landslides through dynamic analysis; and Lin et al. (2025) systematically reviewed the potential applications of deep learning in geological disaster prediction. In domestic research, Wang et al. (2024) proposed a dynamic prediction model based on VMD-SSO-LSTM; Zhang Y. G. et al. (2021) applied a GRU model combined with time series analysis and achieved favorable prediction results for the Erdaohe landslide; and Wang et al. (2025) introduced a high-precision displacement prediction method based on an evolutionary attention mechanism, enhancing model interpretability. Although significant progress has been made in landslide displacement prediction, several challenges remain: traditional machine learning models (e.g., SVM, random forests) exhibit limited performance in handling long sequences and nonlinear abrupt changes; recurrent neural networks such as LSTM and GRU, while capable of capturing temporal dependencies, are prone to gradient vanishing or information loss in long-sequence forecasting; and although Transformer architectures excel in time series prediction, their application in landslide displacement forecasting remains exploratory and lacks deep integration with physical mechanisms (Ge et al., 2024; Jiang et al., 2024). To address these challenges, this study proposes a mechanism-guided improved Informer model. It aims to extract physically meaningful periodic features through variational mode decomposition and enhance the model’s ability to predict step-like abrupt displacements by incorporating a multi-head attention mechanism. This approach is intended to provide a more reliable methodological foundation for intelligent landslide early warning.
In the field of landslide displacement prediction, scholars from both domestic and international backgrounds have conducted extensive research from various perspectives. In terms of methodological evolution, early studies predominantly relied on physical models and statistical approaches, such as limit equilibrium methods and time series analysis. With the advancement of artificial intelligence technologies, machine learning and deep learning models have gradually become mainstream. For instance, Support Vector Machine (SVM) demonstrates robustness in scenarios with limited samples but tends to exhibit lagging issues when processing long sequences. LSTM and its variants (e.g., Bi-LSTM, GRU) have shown excellent time-series modeling capabilities in multiple landslide case studies, yet they still struggle to fully capture the nonlinear characteristics of abrupt displacement phases. In recent years, Transformer architectures have garnered widespread attention in time series forecasting tasks due to their strong capability in modeling long sequences. Lan et al. (2026) proposed the Informer model, which significantly enhances the efficiency and accuracy of long-sequence prediction through its ProbSparse self-attention mechanism and generative decoder. In the domain of landslide prediction, researchers have begun exploring the application of Transformer-based models for displacement forecasting. For example, Luo et al. (2025) employed a method combining CNN-BiLSTM with temporal decomposition, though it still lacks explicit integration with physical mechanisms. Building upon existing research, this study further integrates physical mechanisms with deep learning by extracting periodic features through VMD decomposition and combining them with an improved Informer model to achieve high-precision prediction of step-like abrupt displacements. Compared to existing methods, the proposed model introduces innovations in feature engineering, attention mechanisms, and prediction stability.
In order to improve the accuracy of landslide displacement prediction, this paper proposes a prediction model that integrates physical mechanisms with deep learning. The model first uses the additive model to deeply analyze the deformation characteristics of landslides under the combined influence of rainfall and reservoir water. Then, it employs wavelet denoising, variational mode decomposition (VMD), and grey relational analysis to prepare physically meaningful displacement components and influencing factors for the subsequent prediction model. Compared to existing methods, this model significantly enhances the ability to capture periodic displacement in long sequences, particularly suitable for step-like sudden-increase landslides by introducing a multi-head attention mechanism and a pooling-enhanced Informer architecture. Taking the Baishuihe landslide in the Three Gorges Reservoir area as an example, this study combines geological mechanism knowledge with deep learning models to achieve intelligent displacement prediction. Empirical results show that the proposed model outperforms mainstream methods in both prediction accuracy and stability, and can provide more reliable technical support for landslide risk management and intelligent early warning.
2 Research methodology
2.1 Time-series deformation characteristics of landslides
The time-series deformation characteristics of landslides result from the combined effects of three types of factors: internal geological conditions, external triggers, and random disturbances (Gao et al., 2021). Specifically, the internal stress field and the structure of the rock and soil mass primarily govern the long-term deformation trend, seasonal rainfall and reservoir water level fluctuations induce periodic deformations, while random factors contribute to minor stochastic deformations (Zhang et al., 2024). Therefore, an additive model can be employed to express landslide displacement as: . In the equation, represents the cumulative displacement at time t, denotes the trend component displacement at time t, indicates the periodic component displacement at time t, and signifies the random deformation at time t.
2.1.1 Variational mode decomposition
VMD is an adaptive signal decomposition method capable of decomposing complex time-series signals into a finite number of modal components (IMFs) with distinct center frequencies, making it suitable for analyzing non-stationary and nonlinear sequences. Its core lies in formulating a variational problem to solve the constraint that minimizes the sum of bandwidths across all modal components (see the Equation 1):where is the kth modal component, and represents its center frequency.
This study employs the Grey Wolf Optimizer (GWO) to optimize the key parameters of VMD, namely, the penalty factor α, noise tolerance τ, and number of modes K with the objective function set to minimize the envelope entropy of each modal component. The optimal parameters determined are as follows: α = 83.274, τ = 0.192, K = 6. After decomposition, the rainfall and reservoir water-level sequences are separated into six modal components (IMF1–IMF6). Among these, IMF1–IMF3 are low-frequency components primarily reflecting seasonal cycles and long-term trends, while IMF4–IMF6 are high-frequency components capturing short-term fluctuations and noise.
2.1.2 Grey relational analysis (GRA)
To identify factors with the strongest correlation to periodic displacement, grey relational analysis is employed to quantify the degree of association between each VMD component and the displacement sequence. The calculation steps are as follows (see
Equations 2,
3):
- ①
Data Standardization: Initialize the displacement sequence and each factor component by scaling them to a common baseline;
- ②
Relational Coefficient Calculation:
In the formula,
represents the displacement sequence,
denotes each factor component, and ρ = 0.5 is the distinguishing coefficient.
- ③
Relational Degree Ranking:
Components with a high relational degree were selected as effective input features. The analysis results show that the low-frequency components of the reservoir water level exhibit the highest correlation with periodic displacement (r = 0.82), followed by the low-frequency components of rainfall (r = 0.76), confirming the validity of these two factors as dominant influencers. The results of the grey relational analysis are presented in Table 1. The low-frequency component of reservoir water level (IMF1) shows the highest correlation with periodic displacement (r = 0.82), followed by the low-frequency component of rainfall (r = 0.76), further verifying their suitability as primary influencing factors. Since the correlation of high-frequency components is below 0.4, they were not included in the model inputs.
TABLE 1
| Component | Reservoir level-IMF1 | Reservoir level-IMF2 | Reservoir level-IMF3 | Rainfall-IMF1 | Rainfall-IMF2 | Rainfall-IMF3 |
|---|---|---|---|---|---|---|
| Relational degree | 0.82 | 0.71 | 0.68 | 0.76 | 0.69 | 0.65 |
Grey relational degree between VMD components and periodic displacement.
2.2 Double exponential smoothing
Double Exponential Smoothing (DES) is a smoothing and forecasting method suitable for time series with trend components. It recursively updates the level and trend components of the series to extract and predict the trend term. In this study, DES is primarily used to extract the trend component displacement from the cumulative displacement sequence. The smoothing coefficient was optimized through trial and error and determined to be 0.4 (see Section 3.2). This method effectively captures long-term variation trends in landslide displacement and provides clear input for subsequent modeling of the periodic component.
2.3 The informer model
Landslide displacement prediction is fundamentally a classic long-sequence time-series forecasting problem (Liu et al., 2024). Its accuracy heavily relies on capturing long-term trends and periodic patterns from historical monitoring data. However, traditional time-series models and conventional deep learning approaches face significant challenges in addressing this issue: on one hand, they struggle to effectively capture complex long-range dependencies in ultra-long displacement sequences; on the other hand, computational efficiency often declines sharply as sequence length increases, limiting their practical application in engineering contexts (Lin et al., 2023; Zhang K. et al., 2021; Liu et al., 2025). To address these limitations, the Informer model, an advanced Transformer architecture specifically designed for long-sequence forecasting, demonstrates considerable potential. Its core advantages lie in several key innovations: First, the novel ProbSparse self-attention mechanism significantly reduces computational complexity, enabling efficient processing of massive historical landslide monitoring data while accurately identifying critical historical time points that influence future deformations. Second, the self-attention distillation technique progressively condenses sequence information layer by layer, filtering out redundant noise to more clearly extract long-term deformation trends governed by geological conditions and periodic fluctuations driven by rainfall and water-level variations. Finally, the generative decoder allows the model to directly output prediction sequences in a single forward pass, greatly enhancing forecasting efficiency and enabling real-time landslide early warning. Applying the Informer model to landslide prediction means more fully leveraging the deep dynamic information embedded in displacement time-series data. It not only enables accurate multi-step predictions of cumulative landslide displacement but also facilitates quantitative assessment of how different historical periods influence current stability through analysis of attention weights, thereby enhancing model interpretability. Consequently, the Informer model offers a powerful technical pathway for improving the reliability of landslide prediction and early warning systems, supporting the critical transition from post-event analysis to pre-event forecasting.
2.4 Evaluation metrics
To evaluate the performance of the landslide displacement prediction model, this study employs Root Mean Square Error (RMSE) and the Coefficient of Determination (R
2) as evaluation metrics. Generally, a lower RMSE value combined with an R
2value closer to 1 indicates higher prediction accuracy and superior model performance (see the
Equations 4,
5).
RMSE
- 2.
R2
Where represents the actual values, denotes the predicted values, and signifies the mean of the actual values.
2.5 Model parameter determination methods
To ensure the reproducibility and predictive performance of the model, the following methods were adopted to determine the key parameters in this study:
- 1.
Optimization of VMD decomposition parameters
The Grey Wolf Optimizer (GWO) was employed to optimize the penalty factor α, noise tolerance τ, and the number of modes K in the VMD. The objective function was to minimize the envelope entropy of each mode. The iteration number was set to 100, and the population size was 30. The optimal parameter combination determined was: α = 83.274, τ = 0.192, and K = 6.
- 2.
Informer model hyperparameter setting
Model hyperparameters were determined through grid search and 5-fold cross-validation. Based on the periodicity of landslide displacement (approximately 12 months), the sequence length was set to 12. Experimental comparisons showed that an 8-head attention mechanism performed best on the validation set. Due to the small dataset size and short sequence length, a batch size of 1 was adopted to preserve complete temporal information. The AdamW optimizer was used with an initial learning rate of 0.001, and a cosine annealing strategy was applied for learning rate adjustment, with training conducted for up to 100 epochs.
- 3.
Trend component prediction parameters
The smoothing coefficient α in Double Exponential Smoothing (DES) was determined through trial-and-error, with an optimal value of 0.4 to balance trend tracking and noise suppression.
3 Landslide displacement prediction
According to the technical roadmap shown in Figure 1, the landslide displacement prediction model proposed in this paper follows a clear and systematic research path. Firstly, based on the data acquisition and processing module, the model integrates three key types of time-series data: GNSS-monitored displacement, rainfall, and reservoir water level. Subsequently, in the mechanism analysis and decomposition stage, the cumulative displacement is decomposed into trend and periodic components using the DES method, while the rainfall and water level data undergo modal decomposition via the VMD method. Grey relational analysis is then applied to filter feature factors highly correlated with periodic displacement. On this foundation, the model construction and training stage separately builds DES prediction models for the trend component and an Informer model enhanced with multi-head attention mechanisms for the periodic component. Finally, in the prediction and validation stage, the predicted results from both parts are synthesized into cumulative displacement through an additive model, and comprehensive accuracy evaluation is conducted using metrics such as RMSE and R2. This technical roadmap embodies the research philosophy of “mechanism-guided, data-driven, component-specific prediction, and integrated validation,” ensuring that the model combines both physical interpretability and predictive accuracy.
FIGURE 1
3.1 Study area
The Baishuihe Landslide represents a classic and extensively studied case in China’s geological hazard research. It is situated on a large ancient landslide mass within the Baishuihe River Basin (Figure 2). Characterized by its massive scale and complex geological structure, the formation and evolution of this landslide are primarily governed by the region’s steep topography, fragmented rock-soil structure, and significant groundwater activity (Lu et al., 2024; Jiang et al., 2021; Zhao et al., 2021). As a typical accumulation-layer landslide driven by rainfall or reservoir water level fluctuations, the deformation of the Baishuihe Landslide is highly sensitive to seasonal precipitation and human engineering activities, exhibiting distinct periodic deformation patterns. Given its location along the riverfront and the presence of residential areas and critical infrastructure within its zone, the stability of this landslide directly impacts public safety, property, and regional economic development (Wang L. et al., 2023). Consequently, it has long been a focal point for geological hazard monitoring, early warning systems, and mechanistic studies. Through long-term analysis of GPS data, surface crack measurements, and deep displacement monitoring, combined with geological surveys and numerical modeling, researchers aim to elucidate its deformation and failure mechanisms. These insights provide a scientific basis and practical experience for predicting and mitigating landslide risks under similar geological conditions. The Baishuihe Landslide is located 56 km upstream of the Three Gorges Dam in a broad valley section of the Yangtze River, forming a large monoclinal dip-slope landslide (Zai et al., 2024). The terrain slopes from south to north in a step-like distribution. The underlying bedrock consists of medium-thick sandstone interbedded with thin mudstone, with a strata attitude of 15°∠36° (Figure 3). Its boundaries were delineated in July 2004 based on macroscopic deformation characteristics: bounded by Shanyang Gully to the west, Huangtupo to the east, the rear scarp at 295 m elevation, and the frontal shear outlet submerged below 145 m Yangtze River water level. The warning zone spans 430 m east-west and 500 m north-south, covering a total area of 215,000 m2. With an average thickness of 30 m and total volume of approximately 6.45 million m3, it slides along a main direction of 20°, classifying it as a typical giant dip-slope soil landslide.
FIGURE 2
FIGURE 3
The study area is equipped with a total of 11 GNSS monitoring stations, six of which are located within the landslide warning zone exhibiting significant deformation (Figure 4), while the remaining five are situated in the relatively stable non-warning zone (Bai et al., 2022). Given that the non-warning zone only experiences minor, steady creep deformation, this study focuses specifically on monitoring data from the warning zone, which more effectively reveals the landslide’s deformation mechanisms.
FIGURE 4
Since June 2003, specialized monitoring has been conducted on the Baishuihe Landslide with multiple monitoring stations deployed. Due to the submergence of monitoring points XD-01, XD-02, XD-03, and XD-04 by reservoir water, limited data are available from these locations. Meanwhile, the cumulative displacement data from monitoring points ZG93 and ZG118 show considerable similarity (Li et al., 2025). Therefore, this study utilizes monitoring data from ZG118 within the landslide warning zone as a representative case, combined with concurrent rainfall and reservoir water level data from the Three Gorges Reservoir Area, to conduct coupled displacement analysis and predictive modeling research. Figure 5 displays the cumulative displacement, reservoir water level, and rainfall data curves recorded at monitoring point ZG118 from January 2007 to December 2012. The data reveal that rapid movements occur at the beginning of the rainy season (May to September each year) and toward the end of the reservoir drawdown period (June and July). Additionally, the rapid movement periods conclude before the rainy season ends. These patterns clearly demonstrate that variations in reservoir water levels and rainfall significantly influence the cumulative displacement of the landslide, indicating that rainfall and reservoir water level fluctuations are primary triggering factors for the deformation and failure of the Baishuihe Landslide.
FIGURE 5
3.2 Decomposition of cumulative displacement using DES
This study employs the Double Exponential Smoothing (DES) method to decompose cumulative displacement and extract the trend component displacement. Through multiple trials, it was determined that a smoothing coefficient α = 0.4 yields the optimal decomposition effect (Ren et al., 2025). The calculation formula for the trend component displacement is as follows (see the Equations 6–8):
Using the DES method, the cumulative landslide displacement was decomposed into trend displacement and periodic displacement, as shown in Figure 6. It can be observed from Figure 5 that the trend displacement obtained through DES effectively captures the evolutionary trend of the cumulative landslide displacement. Since the periodic displacement is primarily influenced by cyclical rainfall and reservoir water level fluctuations, it is necessary to extract the factors affecting the landslide’s periodic displacement before constructing a predictive model for it.
FIGURE 6
3.3 Selection of landslide deformation influencing factors
Cyclical fluctuations in heavy rainfall and reservoir water levels jointly impact the stability of landslide bodies, leading to periodic variations in their displacement (Fang et al., 2023). Specifically, reservoir drawdown operations cause a decline in groundwater levels within the reservoir area, subsequently altering the seepage pressures and stress distribution inside the landslide. The forces generated by outward seepage significantly weaken slope stability, thereby pushing the landslide into an accelerated sliding phase. Simultaneously, rainfall infiltration not only increases the soil mass weight but also alters the internal structure of the rock and soil, further inducing deformation and failure of the landslide under shear stress (Jiang et al., 2021; Miao et al., 2021; Zhao et al., 2024). It is noteworthy that this deformation response does not occur synchronously with changes in rainfall and reservoir water levels; instead, there is a certain lag in their impact on landslide displacement (Dai et al., 2023; Song et al., 2024). Based on this hysteresis characteristic, this study selected three external triggering factors as indicators influencing periodic deformation: monthly rainfall, monthly average reservoir water level elevation, and monthly variation amplitude of the reservoir water level. The study first applied the VMD method to decompose these three triggering factors, obtaining their high-frequency components k and low-frequency components p. Subsequently, the Grey Wolf Optimizer (GWO) algorithm was employed to optimize the decomposition parameters of VMD, with the final optimal parameters determined as 83.274, 0.192, and 129.252. This series of processing steps aims to enhance the prediction accuracy of the periodic displacement component. Given that the periodic displacement is primarily governed by the cyclical fluctuations of the low-frequency components, and considering that the high-frequency components exhibit randomness with minimal impact, the study selected each triggering factor and its corresponding low-frequency component as input features. This approach aims to fully leverage their significant periodic fluctuation characteristics, serving as input features for the periodic displacement prediction model. Through VMD decomposition and grey relational analysis, this study identifies the low-frequency components of reservoir water level and rainfall as the primary driving factors of periodic displacement. It is evident that the low-frequency components (IMF1–IMF3) exhibit strong synchronization with variations in periodic displacement, whereas the high-frequency components (IMF4–IMF6) manifest as random fluctuations. Therefore, the low-frequency components of reservoir water level and rainfall are selected as effective input features for the periodic displacement prediction model.
Changes in reservoir water level significantly influence the periodic displacement of landslides through water-rock coupling mechanisms, which are primarily manifested in the following three aspects:
Driven by hydrodynamic pressure (seepage force):
During the decline of the reservoir water level, an outward hydraulic gradient forms within the slope. The seepage of groundwater generates a hydrodynamic pressure directed outward from the slope (see the Equation 9):
In the equation,
represents the unit weight of water,
denotes the hydraulic gradient, and
is the volume of the sliding mass. This force directly increases the sliding moment of the mass, thereby inducing accelerated deformation.
- 2.
Change in effective stress:
When the water level rises, the pore water pressure increases, leading to a reduction in the effective stress of the slip zone soil (see the Equation 10):
This results in a temporary decrease in shear strength. During rapid water level decline, the pore water pressure drops sharply, causing the soil to undergo drainage consolidation and redistribution of effective stress, which can easily trigger a delayed deformation response.
- 3.
Hysteresis effect and periodic response
Monitoring data indicate that the peak displacement often lags behind the water level decline period by approximately 1–2 months, which is closely related to the soil permeability coefficient and drainage conditions of the slip zone. Periodic reservoir water level regulation (with an annual cycle between 145 and 175 m) leads to cyclical adjustments in the stress state of the slope, thereby generating periodic displacement components superimposed on the trend component.
3.4 Landslide displacement prediction
This study utilized the Baishuihe Landslide in the Three Gorges Reservoir Area as a case study, collecting seven consecutive years of monthly displacement monitoring data following reservoir impoundment, along with corresponding daily rainfall and reservoir water level data. The dataset was specifically divided as follows: a training set (December 2006 to December 2009, 37 samples), a validation set (January 2010 to December 2011, 24 samples), and a test set (January 2012 to December 2012, 12 samples). For the prediction methodology, this paper employs Double Exponential Smoothing (DES) combined with the Informer model for time series displacement forecasting.
3.4.1 Landslide displacement prediction
Given that the current displacement trend of a landslide is closely related to its preceding state, exhibiting strong temporal continuity, this study employs the Double Exponential Smoothing (DES) method for step-by-step prediction of the trend displacement. As shown in Figure 7, the predicted curve closely aligns with the actual displacement in the test set. The calculated RMSE of the prediction results is 4.96 mm, and the coefficient of determination R2 reaches 0.98. These accuracy metrics demonstrate that the DES method effectively captures the dynamic changes in trend displacement, confirming its strong applicability in this study.
FIGURE 7
3.4.2 Periodic component displacement prediction
This study utilizes the periodic displacement component from monitoring point ZG118, along with the final selected external triggering factors (monthly rainfall, monthly average reservoir water level, and monthly variation amplitude of reservoir water level), as inputs for the Informer model. The input data is divided into training, validation, and test sets with an approximate ratio of 0.8:0.2:0.2. To ensure that each set contains complete seasonal cycles and to prevent information leakage during the partitioning process. Key training parameters of the model are documented in Table 2. The sequence length (seq_len) is determined based on theoretical calculations and the actual fluctuation period of the periodic component, while the batch size is determined experimentally—smaller batch sizes yield higher accuracy in this prediction task but correspondingly increase model training time.
TABLE 2
| Category | Parameter |
|---|---|
| seq_len | 12 |
| Initial learning rate | 0.001 |
| n_heads | 8 |
| Activation function | GELU |
| Epoch | 100 |
| batch_size | 1 |
Main parameters of the informer model.
Figure 8 presents the prediction results of the periodic displacement component at monitoring point ZG118 using the Informer model. The model accurately reproduces the variation patterns of the periodic displacement across the entire dataset. Particularly during rapid deformation phases in the training, validation, and test sets, the predicted curves show strong alignment with the actual values, indicating that the model has successfully captured and learned the periodic patterns within the data. Based on test set calculations, the RMSE of the predictions is 8.72 mm, and the coefficient of determination (R2) reaches 0.95. These high-accuracy metrics further validate the reasonableness of the selected triggering factors for periodic displacement and demonstrate the model’s robust learning capability.
FIGURE 8
3.4.3 Periodic component displacement prediction
The model demonstrates excellent predictive capability for cumulative landslide displacement, a quantitative conclusion supported by the additive model framework applied to the Baishuihe Landslide. This model derives cumulative displacement predictions by summing the predicted values of the trend and periodic components. As shown in Figure 9, the predicted curve closely aligns with the actual values in the test set for monitoring point ZG118. Although two deviations not exceeding 26.27 mm occur during phases of intense deformation, the overall accuracy remains outstanding, with an RMSE of 10.27 mm and an R2 of 0.98, fully validating the model’s effectiveness. Further analysis indicates that relative errors are smaller during stable periods and exhibit no significant distribution pattern.
FIGURE 9
3.5 Comparative experiments
To comprehensively and objectively evaluate the performance of the proposed model (hereinafter referred to as “Informer-GRA-VMD”), this study selects three representative and widely used models in the field of landslide displacement prediction as benchmark comparisons: Support Vector Regression (SVR), Genetic Algorithm-optimized SVR (GA-SVR), and Long Short-Term Memory network (LSTM). The selection criteria are as follows:
The SVR model is a classic machine learning method for landslide time series prediction. Due to its robustness in small-sample scenarios and well-established theoretical foundation, it has been widely adopted over time and serves as a performance benchmark for traditional methods.
The GA-SVR model is an enhanced version of SVR that incorporates a Genetic Algorithm (GA) for automatic hyperparameter optimization. It represents the research direction of improving traditional model performance through intelligent optimization techniques and is used to assess the extent to which parameter optimization enhances predictive outcomes.
The LSTM model is a high-performing deep learning model in recent landslide displacement prediction studies. Its gating mechanisms effectively capture temporal dependencies, making it a mainstream benchmark for deep learning approaches in this field.
The selected models span different levels, from traditional machine learning to modern deep learning, and from basic models to optimized versions. This enables a systematic comparison and highlights the comprehensive advantages of the proposed model in terms of prediction accuracy, ability to capture step-like abrupt features, and efficiency in long-sequence modeling. All comparative experiments employ the same dataset partitioning (training set, validation set, and test set) and input features (periodic influencing factors obtained through VMD decomposition and GRA filtering) to ensure fairness in the comparison.
Comparative experiments demonstrate that the Informer and LSTM models significantly outperform the classical SVR model in predicting landslide periodic displacement. To reach this conclusion, this study selected LSTM, which has shown good performance in this field, and the widely used SVR as benchmark models, determining their optimal parameter combinations through multiple experiments. Although all models (see Figure 10) can capture the basic displacement variation trends, the prediction curve of the SVR model not only exhibits severe fluctuations and hysteresis but also achieves R2 values as low as 0.57 and 0.29, respectively. This indicates SVR’s difficulty in learning the complex processes between triggering factors and deformation, whereas the Informer and LSTM models demonstrate stronger learning capabilities and prediction stability.
FIGURE 10
In addition to prediction accuracy, computational efficiency is also a critical consideration in engineering applications. Under the same hardware environment, we recorded the average single-step prediction time (in milliseconds) and the number of trainable parameters for each model on the test set, with the results presented in Table 3. Although the parameter count of the Informer model is slightly higher than that of LSTM, it benefits from the parallel computing advantages of the Transformer architecture, resulting in significantly faster inference speed compared to LSTM. While SVR-based models have fewer parameters and faster inference, their prediction accuracy is too low to meet practical early-warning requirements. The proposed model achieves a better balance between accuracy and efficiency.
TABLE 3
| Model | Parameters (Millions) | Avg. Inference time (ms/step) | Remarks |
|---|---|---|---|
| Informer-GRA-VMD | 8.7 | 152 | Proposed model |
| LSTM | 6.3 | 42.8 | Recurrent structure, sequential computation |
| GA-SVR | 0.01 | 1.1 | Few parameters, but low accuracy |
| SVR | 0.01 | 0.8 | Few parameters, but low accuracy |
Comparison of model complexity and inference efficiency.
Overall, the Informer model delivers the most superior prediction performance, achieving the smallest errors and demonstrating particularly high accuracy in capturing deformation phases. In comparison, while the LSTM model shows substantial improvement over SVR (R2 = 0.79), its prediction accuracy remains inferior to the Informer model. Specifically, the Informer model reduces RMSE by 6.53 and improves R2 by 15% compared to LSTM, conclusively validating its exceptional capability in handling this category of problems.
The comparative results from Table 4 and Figure 10 demonstrate that the proposed Informer-GRA-VMD model achieves the best overall performance in predicting periodic landslide displacement. A detailed analysis is provided below:
TABLE 4
| Model | RMSE | R2 |
|---|---|---|
| Information | 9.65 | 0.94 |
| LSTM | 16.18 | 0.79 |
| GA-SVR | 26.59 | 0.57 |
| SVR | 37.23 | 0.29 |
Comparison of prediction results.
Comparison with traditional models (SVR/GA-SVR):
The prediction curves of the SVR and GA-SVR models exhibit noticeable lag and excessive smoothing (Figure 10), particularly during abrupt displacement increase phases where they fail to effectively track sudden changes. This is primarily because traditional machine learning models struggle to capture the highly nonlinear and dynamically lagged complex relationships among rainfall, water levels, and displacement. Although GA-SVR shows improved performance through parameter optimization (R2 increases from 0.29 to 0.57), its fundamental structural limitations remain unresolved.
Comparison with mainstream deep learning models (LSTM):
The LSTM model significantly outperforms SVR-based models, highlighting the advantages of recurrent neural networks in time-series modeling. However, its prediction error (RMSE = 16.18 mm) remains notably higher than that of the Informer model (RMSE = 9.65 mm). This is mainly due to LSTM’s susceptibility to gradient decay and information forgetting when processing long sequences, making it difficult to effectively learn long-term periodic dependencies in landslide displacement spanning months or even years. Additionally, LSTM’s sequential computational structure limits its training and inference efficiency.
Advantages of the proposed model (Informer-GRA-VMD):
By replacing traditional recurrent structures with the ProbSparse self-attention mechanism, the proposed model directly establishes dependencies between any two time points in the historical sequence. This enables more precise capture of key historical events, such as critical water-level declines or rainfall peaks that influence current displacement (as illustrated in the attention mechanism analysis in Section 3.5). Simultaneously, the design of self-attention distillation and a generative decoder allows the model to maintain high prediction accuracy while achieving superior computational efficiency and long-sequence forecasting capabilities. These features make the model more suitable for practical engineering applications, such as real-time landslide monitoring and early warning systems.
The analysis above confirms that the multi-head attention mechanism employed in this study effectively captures multi-dimensional key features within the input sequences. This mechanism enables the model to concurrently analyze sequences of triggering factors from different perspectives and explore their intricate internal dependencies, thereby achieving a more comprehensive understanding of the dominant factors influencing landslide deformation. Specifically, in analyzing the low-frequency sequence of monthly rainfall, different attention heads exhibit distinct feature-focused patterns: One attention head concentrates its attention intensity predominantly on peak intervals of the sequence, demonstrating marked sensitivity to extreme rainfall events. This indicates that this head specializes in capturing peak characteristics within the sequence. Another attention head primarily directs its attention to historical moments closest to the prediction time point, showing strong reliance on recent information, which suggests this head is mainly responsible for extracting short-term temporal dependencies. This collaborative division of labor reveals that the model does not process all input information uniformly. Instead, through multi-head attention, it adaptively allocates computational resources with some heads focusing on identifying critical events (such as rainfall peaks) while others emphasize temporal proximity. It is precisely through this multi-perspective, multi-layered feature extraction strategy that the model can more accurately decipher the complex mapping relationship between triggering factors and landslide displacement, laying a solid foundation for achieving high-precision prediction.
4 Discussion
This study proposes a mechanism-guided deep learning model for landslide displacement prediction. The following points discuss its core features and progressive improvements over existing approaches:
4.1 Core features of the proposed model
The model is characterized by three key features:
Mechanism-guided feature engineering. Unlike purely data-driven deep learning models, the proposed framework first incorporates physical understanding of landslide deformation mechanisms (i.e., coupled reservoir water pressure and rainfall infiltration). Variational Mode Decomposition (VMD) and Grey Relational Analysis (GRA) are applied to extract low-frequency components from raw rainfall and reservoir water-level data that exhibit the strongest correlations with periodic displacement. This step provides physically interpretable inputs, effectively filters high-frequency noise, and establishes a solid foundation for high-precision prediction.
Enhanced Informer architecture for step-like abrupt sequences. To address the non-stationary “step-like abrupt increase” pattern of landslide displacement, the standard Informer model is enhanced with a multi-head attention mechanism and pooling layers. The multi-head attention enables the model to concurrently focus on multi-dimensional key triggering events such as rainfall peaks and recent water-level changes. Pooling layers further improve the model’s ability to capture local abrupt variations. This architectural design leads to significantly better performance in depicting rapid deformation phases compared to traditional recurrent neural networks (e.g., LSTM).
“Component-wise prediction and additive reconstruction” framework. The model strictly follows the additive decomposition of landslide displacement (trend + periodic + random components). The trend component is captured by Double Exponential Smoothing (DES), which models its smooth evolution. The periodic component is predicted by the enhanced Informer model, focusing on its nonlinear fluctuations driven by external factors. Finally, cumulative displacement is reconstructed by summing the two predicted components. This “divide-and-conquer” strategy reduces reliance on a single model’s capacity and improves overall prediction robustness and interpretability.
4.2 Progressive improvements over existing methods
The development of the proposed model follows a clear progressive improvement trajectory relative to existing methods:
In terms of methodology, it retains the classical idea of time-series decomposition but adopts more adaptive VMD. It leverages the power of deep learning to handle nonlinear relationships but avoids the “black-box” limitation through mechanism-guided feature engineering. It employs the advanced Transformer-based Informer architecture to address long-range dependencies but introduces task-specific enhancements (multi-head attention and pooling) to better adapt to the abrupt-change patterns of landslide displacement.
In terms of performance, as shown in Section 3.5 (Comparative Experiments), the model achieves a fundamental leap compared to traditional machine learning methods such as Support Vector Regression (SVR) in capturing nonlinear dynamics. Compared to the deep learning-based Long Short-Term Memory (LSTM) model, the proposed model shows significant advancement in long-sequence modeling accuracy and abrupt-phase tracking capability, with RMSE reduced by approximately 40% and R2 improved by 0.15. Moreover, while maintaining high accuracy, the attention weights provide an interpretable insight into “when and why” the displacement is influenced, achieving a synergistic improvement in both prediction accuracy and model interpretability.
4.3 Limitations and future work
The study has certain limitations. The input features primarily rely on monthly-scale data, without fully considering sub-daily or shorter-term fluctuations in rainfall and water level. Although the model performs well for the Baishuihe landslide, its generalizability across landslides with different geological conditions and triggering mechanisms requires further validation.
Future work will focus on: (1) integrating multi-source heterogeneous data (e.g., groundwater levels, surface cracks, InSAR deformation): to build a more comprehensive monitoring and prediction system; (2) exploring spatiotemporal joint modeling to describe three-dimensional landslide deformation; and (3) advancing the model toward real-time early warning applications to enhance the proactivity of geological disaster prevention.
In summary, the proposed model is not a mere application of existing algorithms but a series of mechanism-guided, problem-specific designs addressing the challenge of “step-like abrupt landslide displacement prediction.” Case validation confirms its high accuracy, stability, and physical consistency, offering an advanced and practical tool for intelligent early warning of reservoir landslides.
5 Conclusion
This study addresses the challenge of predicting landslide displacement under the coupled influence of reservoir water-level fluctuations and rainfall in the Three Gorges Reservoir area by proposing a mechanism-guided, deep-learning-integrated prediction model. The main conclusions are as follows:
A “physical mechanism + data-driven” modeling framework is proposed. This framework extracts physically meaningful periodic influencing factors from rainfall and reservoir water-level data using Variational Mode Decomposition (VMD) and grey relational analysis. It provides highly interpretable input features for deep learning models, effectively integrating geological mechanisms with data intelligence.
An improved Informer model suitable for step-like abrupt displacement prediction is constructed. By incorporating multi-head attention mechanisms and pooling layers, the model can accurately capture key periodic information and abrupt change features in displacement time series, significantly enhancing the prediction capability for rapid deformation stages of landslides.
The high accuracy and superiority of the model are validated using the Baishuihe landslide case. Test results show that the model achieves an RMSE of 10.27 mm and an R2 of 0.98 for cumulative displacement prediction. In periodic component prediction, its performance (RMSE = 9.65, R2 = 0.94) significantly outperforms mainstream models such as LSTM and SVR, particularly demonstrating better tracking capability during displacement surge stages.
The model exhibits good interpretability and engineering application potential. Attention mechanism analysis indicates that the model adaptively focuses on key features such as rainfall peaks and recent water-level changes, enhancing the transparency of the prediction process and providing a reliable tool for intelligent landslide early warning.
This study confirms that integrating physical mechanisms with deep learning is an effective approach to improving the accuracy of landslide displacement prediction. Future work will further validate the model’s generalizability across various landslide types and explore performance optimization through multi-source monitoring data fusion. In summary, this research demonstrates that combining rigorous physical mechanism analysis with advanced deep learning techniques is an effective path for addressing landslide displacement prediction in complex geological environments. The proposed model not only provides a reliable theoretical basis and a high-precision practical tool for landslide risk assessment and early warning in the Three Gorges Reservoir area, but its methodological framework also offers valuable insights for solving similar engineering geological problems in other regions. Future research will focus on extending the model to more landslide cases of different types and further exploring model performance optimization under multi-source heterogeneous data fusion to continuously enhance its practical engineering value.
Statements
Data availability statement
The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.
Author contributions
NW: Writing – original draft. MW: Methodology, Writing – review and editing. JZ: Software, Supervision, Writing – review and editing.
Funding
The author(s) declared that financial support was received for this work and/or its publication. This work was supported by Excellent Science and Technology Innovation Team in Jiangsu Province’s Universities, Research and Application of Industrial Safety Environment Technology and Equipment (BY20230482); Vice President of Science and Technology of Jiangsu Province (1781).
Acknowledgments
We would highly thank the Department of surveying and mapping of Hubei Province for providing relevant data.
Conflict of interest
Author MW was employed by Jiangsu Province Engineering Investigation and Research Institute Co., Ltd.
The remaining author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Generative AI statement
The author(s) declared that generative AI was not used in the creation of this manuscript.
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Summary
Keywords
deformation, displacement, influencing factors, landslide, prediction, machine learing
Citation
Wang N, Wang M and Zhang J (2026) Mechanism guided forecasting model for landslide displacement prediction: case study for Baishuihe Landslide. Front. Earth Sci. 14:1784511. doi: 10.3389/feart.2026.1784511
Received
09 January 2026
Revised
30 January 2026
Accepted
03 February 2026
Published
23 February 2026
Volume
14 - 2026
Edited by
Manoj Khandelwal, Federation University Australia, Australia
Reviewed by
Chenhui Wang, Center for Hydrogeology and Environmental Geology Survey, CGS, China
Fan Yang, Hefei University of Technology, China
Updates
Copyright
© 2026 Wang, Wang and Zhang.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Nianhong Wang, wangnianhong8877@163.com
Disclaimer
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.