DACLnet: A Dual-Attention-Mechanism CNN-LSTM Network for the Accurate Prediction of Nonlinear InSAR Deformation

Abstract

Nonlinear deformation is a dynamically changing pattern of multiple surface deformations caused by groundwater overexploitation, underground coal mining, landslides, urban construction, etc., which are often accompanied by severe damage to surface structures or lead to major geological disasters; therefore, the high-precision monitoring and prediction of nonlinear surface deformation is significant. Traditional deep learning methods encounter challenges such as long-term dependencies or difficulty capturing complex spatiotemporal patterns when predicting nonlinear deformations. In this study, we developed a dual-attention-mechanism CNN-LSTM network model (DACLnet) to monitor and accurately predict nonlinear surface deformations precisely. Using advanced time series InSAR results as input, the DACLnet integrates the spatial feature extraction capability of a convolutional neural network (CNN), the advantages of the time series learning of a long short-term memory (LSTM) network, and the enhanced focusing effect of the dual-attention mechanism on crucial information, significantly improving the prediction accuracy of nonlinear surface deformations. The groundwater overexploitation area of the Turpan Basin, China, is selected to test the nonlinear deformation prediction effect of the proposed DACLnet. The results demonstrate that the DACLnet accurately captures developmental trends in historical surface deformations and effectively predicts surface deformations for the next two months in the study area. Compared to traditional LSTM and CNN-LSTM methods, the root mean square error (RMSE) of the DACLnet improved by 85.09% and 68.57%, respectively. These research results can provide crucial technical support for the early warning and prevention of geological disasters and can serve as an effective alternative tool for short-term ground subsidence prediction in areas lacking hydrogeological and other related data.

1. Introduction

Nonlinear InSAR (interferometric synthetic aperture radar) deformation refers to the measurement and analysis of land surface deformations that deviate from simple, predictable linear trends. Such nonlinear deformations arise from the complex interplay of dynamic forces affecting surface or subsurface structures, exhibiting patterns that change in unpredictable ways over time. They can be triggered by various factors, including the overextraction of groundwater, the exploitation of underground resources, landslides, urban construction activities, earthquakes, and underground mining operations [1,2,3]. Moreover, they pose severe and even catastrophic risks to ground structures, potentially leading to geological disasters such as ground collapse and large-scale landslides [4]. These phenomena can profoundly impact ecological systems, society, and economies; therefore, it is imperative to predict them accurately, promptly, and efficiently. Geodetic survey methods enable stability surveys and the monitoring of surface deformations with early detection capabilities. Meanwhile, deep learning techniques can learn from monitored surface deformation data for analysis and interpretation purposes while predicting future trends in surface deformations [5]; therefore, integrating geodetic survey methods with deep learning to achieve high-precision monitoring and the accurate prediction of nonlinear surface deformation is a vital frontier issue in contemporary geodesy.

Traditional ground deformation measurement methods, like leveling and GNSS, can achieve high-precision in situ monitoring; however, their spatial resolution is generally low, and they are both time-consuming and labor-intensive. In contrast, interferometric synthetic aperture radar (InSAR) technology has emerged as a crucial technique for monitoring surface deformation due to its advantages, including its high spatial resolution, comprehensive coverage, high monitoring accuracy, and facilitation of efficient, noncontact measurements. It has demonstrated remarkable achievements in various fields, including earthquakes [6,7,8], volcanoes [9,10,11], landslides [12,13,14], urban infrastructure monitoring [15,16,17], mining subsidence monitoring [18,19], and frozen ground deformation monitoring [20,21]. With the increasing abundance of spaceborne synthetic aperture radar (SAR) satellites in recent years [22] and the maturation of InSAR technology [23,24,25], it will play an even more important role in surveying and investigating geological disasters; however, due to the fixed revisit cycle of spaceborne SAR satellites, achieving the dynamic monitoring and timely warning of nonlinear surface deformations is difficult.

In the past decade, deep learning technology has been extensively utilized in time series data analyses [26], showcasing remarkable capabilities in specialized areas such as surface deformation monitoring [27]. Among these techniques, convolutional neural networks (CNNs) and recurrent neural networks (RNNs) have gained widespread adoption in imaging geodesy owing to their excellent performance in image processing and sequence data analyses [28,29]. For example, some researchers have employed convolutional neural network (CNN) technology to detect subtle deformations in volcanoes and successfully predict short-term InSAR deformation maps [29,30]. Furthermore, Prabhakar et al. demonstrated outstanding predictive performance by effectively predicting InSAR time series deformation maps using a multiscale attention-directed RNN method [31]. Meanwhile, as an improved version of RNNs, long short-term memory (LSTM) networks have demonstrated unparalleled superiority in this field [32,33]. Several research teams have validated their efficiency and accuracy in sequence prediction tasks. For example, Chen et al. employed LSTM models to simulate and predict the InSAR deformation time series of Beijing Capital International Airport and compared them with other benchmark models such as multilayer perceptron (MLP) and RNNs; LSTM yielded more accurate outcomes [34]. Similarly, Bao et al. constructed a ground deformation prediction model based on LSTM, specifically for the short-term prediction of severe deformations in the SPIA area of Shanghai Pudong International Airport, successfully revealing the spatiotemporal evolution pattern of ground deformation in the SPIA reclamation area [35].

However, traditional deep learning models have certain limitations when facing long-term sequence dependencies and complex spatiotemporal pattern analyses. Although CNNs perform well in handling various types of data, especially in extracting local features, their inherent limitations in convolutional operations make it challenging to capture long-distance dependencies in time series data [36]. On the other hand, while RNN architectures are designed explicitly for ordered data streams, they often encounter the problem of vanishing or exploding gradients when dealing with long-term dependencies [37,38]. Furthermore, LSTM has greatly improved the issue of long-term memory retention and has achieved significant results in various sequence prediction tasks [32,33,34,35]; however, due to the design of LSTM internal units, the output is constrained within a specific numerical range. Even in the multilayer structure, gradient disappearance is still possible. Constructing large and deep LSTM networks may risk overfitting the model [39,40]. Due to the inherent limitations of the models above, they may face obstacles when addressing prediction tasks involving complex and long-term spatiotemporal evolution characteristics of surface nonlinear deformation. In recent years, transformer models have been proposed as an innovative sequence modeling technique and have gained rapid popularity [41]. With their unique self-attention mechanism, these models can efficiently capture both short-term and long-term dependencies in sequence data, thereby avoiding the vanishing or exploding gradient problem encountered by traditional RNNs when dealing with long-range dependencies.

Despite the extensive utilization of CNN or LSTM models in existing studies for surface deformation prediction on InSAR time series data, there remains a lack of research on quantitatively evaluating and predicting complex nonlinear surface deformation using attention mechanism methods. Although some success has been achieved, research has largely focused on relatively simple deformation patterns. These models typically lack a deep understanding of and precise prediction capabilities for complex nonlinear surface deformation dynamics, especially in large-scale subsidence areas with nonlinear characteristics. Additionally, despite the growing body of deep learning research on subsidence prediction, practical predictive applications for large-area surface deformation are still relatively rare. This is mainly because large-area predictions require models not only to process large amounts of data but also to effectively integrate information across different temporal and spatial scales. Considering the spatiotemporal characteristics of complex nonlinear surface deformation, this study draws inspiration from transformers’ attention mechanism and innovatively constructs a CNN-LSTM model called the DACLnet by integrating dual-attention mechanisms to more accurately simulate and predict surface nonlinear deformation. By integrating dual-attention mechanisms into the CNN-LSTM network and combining it with advanced interferometric point target analysis (IPTA) InSAR technology [42], the DACLnet enhances the focus on crucial nonlinear information, enabling the refined monitoring and accurate prediction of surface nonlinear deformation. Finally, taking the oasis area in the Turpan Basin, Xinjiang, as the experimental region, the DACLnet is employed to predict and test surface nonlinear deformation caused by periodic groundwater exploitation.

2. Methodology

The method mainly includes the following steps: (a) Use advanced IPTA-InSAR technology during the data acquisition stage to obtain the ground deformation time series. (b) Design and construct the DACLnet model. (c) Divide the dataset into training sets and test sets for model training and optimization.

2.1. Deformation Signals Monitored Using Advanced IPTA-InSAR

Permanent scatterer interferometric synthetic aperture radar (PS-InSAR) technology, with its high precision in monitoring land surface deformations, has been widely applied in various surface monitoring scenarios. This technique mainly relies on permanent scatterers (PS points) on the surface, such as artificial buildings and exposed rocks. By analyzing the differences in radar echo signals from these points at different times, it can accurately measure minute deformations of the ground or buildings, with precision up to the millimeter level.

However, PS-InSAR technology faces certain applicational limitations in nonurban areas, especially in regions with dense vegetation and complex terrain. In these areas, due to the scarcity of suitable targets that can serve as PS points, traditional PS-InSAR methods struggle to obtain a sufficient density of PS points for effective monitoring.

To overcome this limitation, we use an improved IPTA-InSAR method [42,43] to monitor nonlinear deformations, thereby enhancing the anti-interference ability of InSAR against spatial–temporal incoherence errors in monitoring geological hazard-prone areas with dense vegetation coverage and increasing the number of effectively monitored points. The data processing flowchart of this method is shown in Figure 1. Specifically, the improved method introduces differential interferometric SAR (DInSAR) based on multiview processing in the traditional PS selection process. This is carried out by processing single-look complex (SLC) images through multiview processing. Subsequently, we set appropriate spatiotemporal baseline thresholds to obtain sufficient interferometric pairs. Then, PS points are selected based on the coherence of the differential interferogram. The differential phase, $\delta {\phi }_{i,j}$, corresponding to two adjacent point targets, $i,j$, is expressed as follows:

$$\delta {\phi }_{i,j}=\frac{4\pi }{\lambda }t∆{\upsilon }_{i,j}+\frac{4\pi }{\lambda }\frac{B_{\perp }{∆z}_{i,j}}{Rsin\theta }+∆{\phi }_{i,j,res}$$

(1)

In the formula, $∆{\upsilon }_{i,j}$ represents the linear deformation rate between two point targets; ${∆z}_{i,j}$ represents the elevation residual between two point targets; $t$ is the time interval; $R, B_{\perp }$, $\theta$, and $\lambda$ are the orbital parameters of the satellite; and $∆{\phi }_{i,j,res}$ represents the differential residual phase between two point targets, primarily including the differences in the atmospheric phase, noise phase, and nonlinear deformation phase between the two points.

During the point selection process, the analysis is focused on the points with low spectral diversity [44] and low amplitude dispersion [45]. In monitoring regions with significant terrain variation, InSAR is considerably affected by terrain-related atmospheric delay errors; therefore, before the regression analysis, we used an iterative removal method for elevation-correlated atmospheric delay signals [42,46] to mitigate their influence on subsequent computations while suppressing this signal in highly coherent point targets within the unwrapped interferogram. Subsequently, we used multivariate linear regression to determine linear deformation, topographic errors, and residual phases.

After linear regression, we employed singular value decomposition (SVD) to extract the original time series displacement. The residual phase obtained after removing linear deformation primarily includes nonlinear deformation, atmospheric delays, and phase noise. As atmospheric delays are highly correlated spatially but less so temporally, and phase noise is random in both space and time, we utilize temporal high-pass filtering and spatial low-pass filtering to suppress atmospheric delays. Ultimately, both linear and nonlinear deformations contribute to the final time series displacement, resulting in the observation of temporal surface deformations.

2.2. CNN-LSTM Model Embedded within Dual-Attention Mechanisms

The DACLnet is a CNN-LSTM network model that integrates a dual-attention mechanism, combining the spatial feature extraction capability of a convolutional neural network (CNN) with the time series processing advantage of long short-term memory (LSTM). The structure diagram of the DACLnet model is depicted in Figure 2. Additionally, it introduces a dual-attention mechanism to effectively focus on recognizing and utilizing features in complex spatiotemporal data. By collaboratively applying the dual-attention mechanism within both the CNN and LSTM layers, the model not only emphasizes crucial local and global information but also identifies and enhances key spatial details and moments in the time series. This significantly reduces interference from irrelevant information and markedly improves the model’s ability to predict complex patterns and sequence data. Furthermore, the dual-attention mechanism grants the DACLnet exceptional adaptability, allowing it to flexibly adjust its focus in response to various types of nonlinear surface deformations, thus enhancing its generalization capability and robustly predicting unknown data. These features make the DACLnet highly effective in the precise prediction of nonlinear surface deformations, demonstrating its capability to efficiently handle and analyze complex data.

In this model, the CNN layer is primarily responsible for extracting the task of local spatial features from the input data. Specifically, the data are fed into a convolutional neural network (CNN), which effectively captures complex information across various spatial dimensions through its multilayered convolutional structure, subsequently transforming it into high-dimensional feature vectors that can be understood and captured using machine learning models. The operation of its convolutional layer can be expressed as follows [47]:

$$y[i]=b+{\displaystyle \sum _{j=0}^{W-1}x}[i+j]\cdot h[j]$$

(2)

where $W$ represents the width of the convolutional kernel (window size), $b$ denotes the bias term, $i$ is the index of the output sequence, $j$ refers to the index of elements in the convolutional kernel, $x[i+j]$ signifies the value of the input sequence at the position of $i+j$, and $h\left[j\right]$ indicates the weight of the convolutional kernel at the position of $j$. This method not only leverages the local information of time series data but also enhances model sensitivity to temporal changes by covering the complete annual cycle with a sliding window, thereby improving prediction accuracy and model generalization ability.

After the CNN successfully extracts the local spatial features of the time series data, it is essential to comprehend the complex dependencies among different time windows or sequences. We employ a multi-head attention mechanism to explore and integrate potential global dependencies between these features. This mechanism transforms these data into a high-quality feature vector set reflecting the overall structural characteristics, meticulously reflecting the overall structural characteristics. Operating on different data segments in parallel, the framework proficiently captures the intricate relationships and interactions among these segments. This parallel processing capability allows the mechanism to analyze complex interactions and correlations both among different time windows and across various sequences. By simultaneously focusing on different time windows or sequences of data in parallel, this mechanism yields crucial insights into the inherent correlations and the inter-relationships among external sequences within the same subsidence time series. This enhanced understanding improves our predictive accuracy and deepens our comprehension of dynamic geological changes.

For each attention head, $h$ (a total of H heads), the Q, K, and V are calculated individually:

$$\begin{array}{l}{Q}_h=X{W}_{Q,h}\\ K_h=X{W}_{K,h}\\ V_h=X{W}_{V,h}\end{array}$$

(3)

Then, the attention score is computed and subsequently normalized:

$$A_h=softmax(\frac{Q_h{K}_h^T}{\sqrt{d_{k,h}}})$$

(4)

Finally, the attention output of each head is obtained:

$$C_h=A_h{V}_h$$

(5)

The outputs of all heads are combined and the ultimate output is derived through a fully connected layer:

$$C=Concat(C_1,C_2,\dots ,C_H)W_O$$

(6)

where $X$ denotes the input sequence; $W_{Q,h},{ W}_{K,h},W_{V,h}$ represent the weight matrices of different heads; $W_O$ corresponds to the weight matrix for the merged fully connected layer; and $d_{k,h}$ signifies the dimension of the key vector.

Although introducing a multi-head attention mechanism can significantly improve the comprehensiveness of feature expression, it may also lead to an exponential increase in the number of feature vectors. Certain data may contribute minimally to the final deformation prediction accuracy or even be redundant; therefore, to ensure computational efficiency and effective resource utilization, we incorporate gating units into LSTM for feature selection and filtering [48]. These units can intelligently identify and eliminate the features with negligible influence on the prediction results, thus simplifying the feature vector set. In LSTM, the “discarding” process is achieved through a forget gate operation, which determines which parts of the cell state should be “forgotten”:

$$f_t=\sigma (W_f\cdot \left[h_{t-1},x_t\right]+b_f)$$

(7)

where $f_t$ represents the retention degree and is the output of the forget gate at the current time step, with a value range between 0 and 1; $\sigma$ is the sigmoid function used to generate activation values between 0 and 1; $W_f$ is the weight matrix of the forget gate; $b_f$ is the bias term of the forget gate; and $h_{t-1}$ is the hidden state from the previous time step and the input at the current time step. The “retention” is accomplished by combining input gates and new candidates’ cell states, which selectively add new information to the cell state.

Subsequently, the feature vectors filtered via LSTM gating units undergo additional recalculations through an attention mechanism. This framework is designed to extract and analyze temporal relationships critical for processing time series data. As a specialized type of recurrent neural network (RNN), LSTM is well equipped to handle long-term dependencies through its internal memory units, which effectively store and transmit relevant information. However, challenges such as vanishing or exploding gradients can still arise, particularly in deeper network architectures. To mitigate these issues, the DACLnet integrates attention strategies within the LSTM layer, which enables the model to focus selectively on the most significant segments of the input sequences at different timesteps. This precise focus improves the accuracy of capturing long-term dependencies in time series data, significantly boosting the model’s predictive accuracy. This process refines a more compact and highly abstract representation of global relationships:

$$A=softmax(\frac{Q{K}^T}{\sqrt{d_k}})$$

(8)

where $d_k$ is the dimension of the key vector.

This batch of optimized feature vectors can be fed into the encoding and decoding layers for deep learning processing. Following deep fusion and mapping through the fully connected layer, the model ultimately generates accurate predictions of surface deformation, thereby achieving the efficient utilization of InSAR time series data while ensuring robustness and accuracy in prediction performance.

2.3. Network Training

Prior to inputting the InSAR time series into the DACLnet model for formal training, we initially filter and preprocess the original time series dataset. The filtering stage includes two steps: (1) eliminating weak subsidence points to exclude data with insignificant changes that may affect the efficiency of model learning and result accuracy and (2) implementing data dilution processing to reduce the overall dataset size, thereby decreasing computational load during processing and training while retaining crucial information for maintaining the integrity and effectiveness of the analysis, ultimately ensuring accurate model training and improving training efficiency. Subsequently, in the data preprocessing stage, the sliding window method is used to extract the time series features from the processed dataset. The size of the sliding window is generally selected to cover a certain time range (e.g., one year), enabling the capture of the periodic and seasonal changes of deformation. Through this method, the subsequences generated by each window can reflect the important features and dynamic variations within the specified timeframe and provide abundant input samples for model training.

During the model training stage, the data are divided into training and testing sets. The former are used for model training, while the latter are employed to evaluate the model’s learning and generalization capability. The root mean square error (RMSE) serves as the loss function for model training, effectively measuring the difference between predicted and actual values. In terms of parameter optimization, the Adam optimizer [49] is adopted, which adaptively adjusts the learning rate and optimizes model parameters based on the gradient’s first-order and second-order moment estimates. Dropout techniques [50] are introduced during model training to prevent overfitting, and cross-validation is used to ensure the stability and generalization of the model across different data subsets. The model constantly learns and adjusts through iterative training to optimize its predictive capacity for dynamic deformation time series.

3. Study Area and Data Processing

3.1. The Study Area

The Turpan Basin is located in the eastern part of the Xinjiang Uygur Autonomous Region, China, adjacent to the Hami depressions in the southern region of the eastern Tianshan Mountains, as shown in Figure 3. It possesses a unique geographical location and exhibits a diverse ecological environment. With an extensive geological history, this basin has undergone multiple geological periods and accumulated abundant rock sequences. Its strata are characterized by substantial sedimentary material and possess significant mineral resources, such as oil and natural gas [51].

The region has a typical inland arid climate, featuring low annual precipitation and high evaporation rates, resulting in significant water evaporation and salt accumulation. The scarcity of local water resources primarily stems from the aridity of the climate. Water resources in the basin mainly rely on the melting snow and ice from the Tianshan Mountains and groundwater extraction. The unique geological hydrological features have given rise to this area’s distinctive landforms and ecosystems. Notably, Aiding Lake, situated at an altitude of −155 m [52], represents the lowest point in China.

The Turpan Basin has developed agriculture and is a crucial production area for grain and cash crops in Northwest China. It is the oldest wine-producing region in China and currently serves as the largest grape and Hami melon production base. Moreover, this area is adorned with thousands of kilometers of traditional water conservancy facilities known as “Karez”, which represent a form of unique, ancient hydraulic engineering designed to combat arid environments; however, with escalating agricultural water demands coupled with declining groundwater levels, there is an alarming prevalence of seasonal overextraction of groundwater for farmland irrigation purposes. Consequently, this unsustainable practice has resulted in prolonged nonlinear surface deformation and disrupted the delicate ecological hydrological balance within the region.

3.2. InSAR Datasets

From the Sentinel-1 satellite, we collected ascending/landing InSAR datasets encompassing data from the Turpan Basin between March 2015 and April 2020 (Figure 3).

Table 1. The image parameters of the study areas.

Frame	Heading	Incidence	Pixel Spacing (Rg × Az)	Time	Number
AT41F135	−9.21°	33.65°	2.33 × 13.95 m	25/03/2015–27/04/2020	122
DT121F449	−170.36°	33.57°	2.33 × 13.95 m	19/03/2015–27/04/2020	107

presents the basic parameters of both the ascending and descending SAR image datasets. The AT41F135 image set was observed from 25 March 2015 to 27 April 2020. The DT121F449 image set was observed from 19 March 2015 to 27 April 2020. The spatial coverage and temporal span of both the ascending and descending orbit data exhibit substantial consistency, which ensures the uniformity of the spatiotemporal reference for deformation results as well as accuracy verification among outcomes.

3.3. Data Processing

The improved IPTA-InSAR technique is employed in this study to sequentially process ascending and descending InSAR datasets, with the results uniformly encoded into the geographic coordinate system of an external DEM. Firstly, we establish the thresholds for temporal and spatial baselines and construct an interferometric pair network based on a small baseline set (Figure 4). Then, based on the minimum cost flow (MCF) phase unwrapping technique [53], “two-pass” DInSAR processing is applied to each interferometric pair with multiple viewing numbers of 20:4 [54,55]. A shuttle radar topography mission (SRTM) digital elevation model (DEM) with a resolution of 30 m [56] was employed to remove the topographic phases. In the DInSAR data processing, point targets with a coherence lower than 0.3 were eliminated. The points with low spectral diversity [44] and low amplitude dispersion [45] were selected for the IPTA analysis. We employed a window-iterative estimation method to mitigate local topographically correlated atmospheric delay errors [42,46]. Finally, the time series deformation results were obtained for each map dataset, as shown in Figure 5.

4. Results

4.1. Monitoring Results

4.1.1. Deformation in the Turpan Basin

We used the improved IPTA-InSAR technique described in Section 2.1. to process the ascending and descending Sentinel-1 satellite data from March 2015 to April 2020. We obtained the time series deformation within the study area (Figure 5). As depicted in Figure 4, the InSAR datasets for rail ascension and rail descent exhibited excellent consistency in their monitoring outcomes, revealing substantial subsidence across the oasis region of the Turpan Basin, especially within the plain oasis area located south of the Flaming Mountains fault zone. To illustrate the temporal–spatial development characteristics of deformation, we selected two feature points, P1 and P2, from regions displaying significant deformation monitored via the ascending and descending rails, respectively (Figure 5c,d). It is evident that both ascending and descending orbit-based time series deformations demonstrate consistent patterns and magnitudes of change. Over the monitoring period, point P1 experienced an accumulated subsidence approaching 500 mm, while point P2 exhibited a cumulative subsidence exceeding 150 mm. The time series deformation reveals an overall subsidence trend in this area with notable nonlinear variation characteristics.

From the spatial and temporal characteristics of deformation, it can be seen that the land subsidence in the oasis area near point P1, closer to the southern Flaming Mountains fault zone, exhibits significantly greater magnitude compared to its vicinity at point P2. This region predominantly comprises extensive farmlands. The water source for agricultural irrigation in the Turpan Basin mainly relies on the melting water from the Tianshan glaciers and precipitation; however, due to the obstruction of the Flaming Mountains fault zone, the effective supplementation of the surface runoff and aquifers in the southern area of the Flaming Mountains fault zone with the Tianshan water source becomes challenging, resulting in a high dependence on groundwater in the agricultural irrigation. Consequently, the continuous overexploitation of aquifers occurs periodically. Consequently, the local land surface shows an overall subsidence trend and exhibits periodic accelerated subsidence characteristics consistent with the agricultural planting and irrigation cycles [57].

4.1.2. Reliability Evaluation of InSAR Results

After preprocessing the ascending data, we obtained a total of 574,662 cumulative subsidence deformation time series, and after similarly processing the descending data, we obtained 596,863 series. To quantitatively evaluate the accuracy of the monitoring results, we converted the deformation velocity results independently calculated from ascending and descending orbits into the vertical direction [58]. Subsequently, we plotted the distribution statistics of the ascending and descending rates, as shown in Figure 6. By comparing the histograms of the ascending rates (blue graph a) with the descending rates (red graph b), we observed that the overall distributions of the two datasets are fairly similar; however, the ascending rates have a larger proportion of data near zero, while the descending data exhibit more significant extreme values.

As shown in Figure 6, the differences in deformation monitoring results between ascending and descending tracks can be attributed to their distinct geometric configurations and atmospheric conditions. To further evaluate and verify the reliability of the data solution results and the effectiveness of our processing methods, we filtered for homonymous points based on latitude and longitude, ultimately selecting 45,002 homonymous points. This selection was followed by the creation of a comparative plot (Figure 6c). The RMSE between AT41F135 and DT121F449 results is 5.7 mm/yr. By performing statistical analysis and fitting procedures, we obtained a linear regression equation of $\mathrm{y}=1.1\mathrm{x}+0.94$, with a coefficient of determination R² of 0.97. Notably, most data points exhibit differences that are less than three times the RMSE (between the black dashed lines in Figure 6c). These findings demonstrate the reliability of the InSAR monitoring results in our study.

4.2. DACLnet Results

4.2.1. Network Training Results

According to the training method described in Section 2.3., we filtered out points with cumulative subsidence of less than 10 mm from the original InSAR deformation time series dataset, resulting in a large-scale deformation dataset containing 574,662 deformation time series. To improve the accuracy and efficiency of model training and prediction, we employed an equidistant data sparsification strategy (interval set to 100) to obtain a dataset containing 5748 deformation time series. Considering the 12-day revisit period of the Sentinel-1 satellite, we input data with a sliding window size of 30 to cover approximately one year of InSAR deformation time series. This window configuration allowed us to better capture the dynamic changes in nonlinear deformation on the Earth’s surface within each window over a continuous year while effectively preserving the seasonality of and annual trends in the data. Subsequently, we randomly divided the initial 70% of the 5748 deformation time series as the training set. We allocated the remaining 30% for testing to ensure a balance between model training accuracy and efficiency. This division ensures that the model can learn key feature patterns of nonlinear surface deformations from a sufficient number of training samples, while the testing set is used to independently assess the model’s generalization performance. This ratio of splitting the training and testing sets follows widely accepted best practices in the field of deep learning, aiming to balance the adequacy and effectiveness of model training with the assessment of its generalization capabilities. Finally, we trained and tested the constructed DACLnet model using the abovementioned dataset.

During model training (as shown in Figure 7), the model is determined to be fully trained based on a downward trend in the loss function. When the loss function rapidly decreases and gradually stabilizes at zero, this typically indicates that the model has learned the intrinsic patterns of the training data, the parameters have been optimized, and the training process is nearing saturation.

During the parameter optimization process, the Adam optimizer is selected due to its adaptive learning rate feature, which dynamically adjusts the learning rate based on the first and second moment estimates of the parameter gradients. This capability accelerates model convergence and demonstrates superior optimization performance when dealing with complex datasets, ensuring the efficient updates of model parameters. For the training process, we utilized the Adam optimizer with a learning rate of 0.005. The entire training process consisted of five epochs, comprising 14,615 iterations. Such settings ensured sufficient exposure to data and facilitated profound learning to accurately capture and predict intricate dynamics within the deformation time series. Additionally, a dropout rate of 0.2 was set during training to mitigate overfitting risks and enhance the model’s generalization ability. This technique enhances the model’s ability to adapt to unseen data by randomly dropping a portion of the neuron outputs, forcing the model to learn more generalized features. To ensure the stability and generalization performance of the model, multiple cross-validations were conducted to ensure the stability and generalization performance of the model. In each iteration, the model assimilated spatiotemporal patterns of the deformation sequence based on the data within the input window to improve the accuracy of surface deformation prediction. Detailed information regarding the key parameters utilized in the model training process is provided in

Table 2. Parameter information for the DACLnet model configuration.

Parameter	Configuration
Optimizer	Adam
Dropout	0.2
Learning rate	0.005
Training epochs	5
Training iterations	14,615
Input window length	30
Output window length	1
Number of attention heads	8

.

4.2.2. Model Performance Testing

To test the performance of the DACLnet, we used the same training scheme to train the existing LSTM and CNN-LSTM models. Evaluation metrics, including the MAE (mean absolute error), RMSE (root mean square error), and MAPE (mean absolute percentage error), were utilized to compare and analyze the prediction results of these three models. The findings demonstrated that the DACLnet model exhibited outstanding performance in predicting nonlinear surface deformation, particularly in capturing complex spatiotemporal patterns and long-term dependencies, as depicted by the black rectangular boxes in Figure 8. The DACLnet more accurately simulated the local fluctuation features of complex time series compared to the pure LSTM and CNN-LSTM models.

The results in

Table 3. Accuracy evaluation results of LSTM, CNN-LSTM, and the DACLnet.

Model	MAE	RMSE	MAPE
LSTM	0.0197	0.0369	0.6103
CNN-LSTM	0.0164	0.0175	0.1345
DACLnet	0.0015	0.0055	0.0750
vs. LSTM	92.39%	85.09%	87.71%
vs. CNN-LSTM	90.85%	68.57%	44.24%

present the MAE, RMSE, and MAPE for each model’s predicted outcomes compared to the actual observations. The LSTM model exhibited a moderate level of prediction accuracy, with MAE, RMSE, and MAPE values of 0.0197, 0.0369, and 0.6103, respectively. It displayed higher error rates than the other models. The CNN-LSTM model effectively captured the spatiotemporal features of the time series data by incorporating convolutional layers, resulting in improved performance with MAE, RMSE, and MAPE values of 0.0164, 0.0175, and 0.1345, respectively. The proposed DACLnet model had MAE, RMSE, and MAPE values of 0.0015, 0.0055, and 0.0750, respectively. Compared to the LSTM and CNN-LSTM models, the DACLnet model exhibited a significant reduction in MAE of 92.39% and 90.85%, RMSE of 85.09% and 68.57%, and MAPE of 87.71% and 44.24%, respectively. By introducing a dual-attention mechanism, the DACLnet effectively enhanced the focus on critical temporal features, thereby improving the accuracy of predicting nonlinear deformations.

4.2.3. Prediction Result

After confirming the prediction reliability of the DACLnet model, we employed it to forecast nonlinear surface deformations in the future. Figure 9 illustrates the projected surface deformations for the upcoming two months utilizing the DACLnet. A comparison with actual observed data indicates that the discrepancy between the predicted outcome for the next two months and the actual observation values remains within a controlled margin of 0.5 mm. This demonstrates a high degree of agreement between the nonlinear deformation predicted with the DACLnet model and the actual observations.

A further analysis of

Table 4. A comparison of prediction errors across different time periods (the data in this table come from the corresponding time points and predicted data of 574,662 deformation time series).

Period	MAE	RMSE	MAPE
12 days	0.0045	0.0068	0.0146
24 days	0.0108	0.0161	0.0318
36 days	0.0151	0.0220	0.0426
48 days	0.0215	0.0306	0.0592
60 days	0.0303	0.0430	0.0823

, which details the DACLnet model’s prediction errors across intervals of 12, 24, 36, 48, and 60 days using metrics such as the MAE, RMSE, and MAPE, indicates that despite a gradual increase in error values over extended periods, the highest MAPE remains notably low at 8.23% at 60 days. The sustained accuracy within acceptable error thresholds underscores the robustness of the DACLnet model for long-term forecasting in infrastructure monitoring and geological assessments. Moreover, this consistent prediction accuracy affirms the model’s practical utility in real-world scenarios.

Figure 10 shows the surface time series deformation rate in the main deformation area of the Turpan Basin, monitored with InSAR and predicted with the DACLnet using IDW (inverse distance weighting) interpolation. The predicted values are highly similar to the actual values in spatial distribution. By analyzing historical data, the DACLnet model can capture the nonlinear characteristics of surface deformation and provide reliable predictions for future deformation trends.

The experimental results demonstrate that the DACLnet model can accurately predict the development trends of nonlinear deformation in the temporal domain and achieve excellent prediction outcomes in the spatial domain, thereby showcasing the robust applicability and accuracy of the DACLnet for predicting nonlinear surface deformation tasks.

4.2.4. Reliability Evaluation of the DACLnet Results

We calculated the observed and predicted deformation rates and then conducted statistical and correlation analyses between the observed deformation rates per subsidence point and the DACLnet prediction results, as shown in Figure 11. The monitoring and prediction results exhibit a strong correlation. The linear regression equation is $\mathrm{y}=0.98\mathrm{x}+0.18$, with an RMSE of 1.01 mm/yr and a correlation coefficient of R² 0.99. Most point discrepancies are less than three times the RMSE (between the black dashed lines in Figure 9). This indicates a high degree of fit between the model and the data, demonstrating robust predictions’ reliability.

5. Discussion

5.1. Analysis of the Temporal Variability in the Correlation between Observed and DACLnet-Simulated Deformations

In Figure 9, we observe variations in the correlation between actual deformations and DACLnet-simulated deformations across different time spans. For the data presented in Figure 8, we employed a differencing method to test for stationarity. We found that data prior to 28 March 2019 did not exhibit stationarity at a 5% significance level, whereas data afterward showed good stationarity. This indicates that the statistical characteristics of the data vary significantly over different periods, which may be one of the main reasons for the changes in the correlation between the simulated and observed data. We believe that the DACLnet model exhibits certain limitations when handling strongly non-stationary data, particularly under rapidly changing environmental conditions, where the nonlinear and non-stationary characteristics of the data can impact the model’s simulation performance.

Furthermore, the seasonal and cyclical characteristics of surface deformations also significantly affect the model’s predictive performance. Surface deformations often show distinct seasonal patterns due to cyclical changes in natural factors, such as precipitation and temperature. Although the DACLnet model captures seasonal features in time series well through its dual-attention mechanism, the predictive accuracy still fluctuates during transitional seasons due to potential limitations in the training data. This limits the model’s performance during specific periods.

5.2. Model Performance and Data Sparsity Issues

In our study, by analyzing the correlation between actual satellite measurement data and predicted position data, we confirmed the reliability and accuracy of the DACLnet model in the short-term prediction of ground subsidence; however, in the accuracy analysis of surface deformation prediction results (see Figure 11), there is a certain deviation between the DACLnet prediction results and the actual observed values for the annual subsidence rates near −150 mm/yr. This discrepancy primarily arises from the limited number of relevant points assessed (see Figure 6), resulting in insufficient deformation data within the dataset, which contains evenly spaced samples. Consequently, during training, the model fails to thoroughly learn the deformation patterns under these exceptional circumstances. In addition, the DACLnet may lack sufficient generalization ability to handle atypical or extreme surface subsidence phenomena. In future research, we will strive to improve the dataset’s balance and completeness to enhance the model’s adaptability and prediction accuracy for complex surface deformation events.

5.3. Long-Term Applicability of the Model and Future Directions for Optimization

Although the DACLnet model, which integrates deep learning and InSAR technology, has shown promising practicability and effectiveness in predicting nonlinear surface deformation, further exploration is needed to assess its applicability in long-term prediction and complex geographical conditions. The extension of the prediction time window may introduce error accumulation that could potentially impact the accuracy of long-term predictions. Additionally, the DACLnet lacks an established internal connection between surface nonlinear deformation and local geological hydrological conditions. This may limit its predictive accuracy under longer time scales and more complex environmental conditions; therefore, the model currently serves as an effective alternative tool for short-term ground subsidence prediction in areas lacking hydrogeological data. In the future, our research will focus on optimizing the model structure and incorporating additional environmental factors to improve the accuracy and robustness of the DACLnet in nonlinear surface deformation prediction.

6. Conclusions

This study proposes a novel DACLnet model to address the challenge of predicting nonlinear surface deformation. By leveraging the spatial feature extraction capability of a CNN and the time series learning advantage of LSTM, along with an intensive focus on crucial information provided by an attention mechanism, it enables an in-depth understanding and dynamic capture of nonlinear deformation features. Through the practical prediction of nonlinear surface deformation in the Turpan Basin, the DACLnet model performs well and accurately in processing complex spatiotemporal series data. Compared with the LSTM and CNN-LSTM models, the DACLnet achieves respective improvements of 85.09% and 68.57% in prediction accuracy for nonlinear deformation (measured using the RMSE of the test set). Moreover, through small-sample learning and training, the DACLnet achieves the high-precision and short-term prediction of large-scale and nonlinear surface deformations, providing a reliable and efficient tool for early dynamic geological disaster warnings, which are crucial for disaster prevention and reduction.