Interpretable Multivariate Landslide Displacement Forecasting Based on InSAR and Deep Learning: PatchTST with Learnable Channel Fusion

Highlights

What are the main findings?

• PatchTST-Fusion improves multivariate MT-InSAR landslide displacement forecasting.
• Learnable channel fusion captures coupled effects of displacement, rainfall, and reservoir water level.

What are the implications of the main findings?

• TimeSHAP reveals feature- and time-specific trigger contributions.
• The framework supports interpretable landslide monitoring and early warning.

Abstract

Accurate time series forecasting is fundamental to geohazard early warning, yet remains a major challenge. Conventional in situ geotechnical monitoring remains costly and spatially constrained, whereas deep learning applied to remote sensing data has become increasingly prevalent but often suffers from opacity of model decision-making. To address this issue, we propose a Transformer-based forecasting framework, namely PatchTST-Fusion, adapted for multivariate Multi-Temporal Interferometric Synthetic Aperture Radar (MT-InSAR) time series. The framework integrates model interpretability analysis through TimeSHAP, providing temporal and feature-level attributions across the input sequence. Landslide deformation time series are first derived from Copernicus Sentinel-1 SAR data. Variational Mode Decomposition is then applied to decompose the non-linear signals into trend, seasonal, and noise components. The denoised displacement series are modeled and forecast using the proposed PatchTST-Fusion, which incorporates rainfall and reservoir water level fluctuations as feature-level drivers. Application to the Daping landslide cluster in the Three Gorges Reservoir Area in China demonstrates that our method captures both the long-term and transient non-linear coupling between deformation and its triggers, surpassing state-of-the-art models including CNN-BiGRU-Attention, Informer and original PatchTST with 7–55% improvements in MAE and 10–52% improvements in RMSE. Beyond predictive gains, feature attribution of environmental triggers via TimeSHAP reveals that rainfall and reservoir regulation exert temporally distinct influences on slope kinematics, with high relative importance concentrated in specific periods and characteristic lagged responses. This interpretable framework provides both enhanced forecasting accuracy and process-based insights, offering a broadly applicable tool for landslide early warning in reservoir regions.

1. Introduction

Due to the broad distribution, high frequency, and severe social and economic impacts, landslide disasters are among the most destructive and widespread geological hazards worldwide [1,2,3]. Landslides occur predominantly in mountainous and hilly regions where complex geological conditions and active tectonics exacerbate instability. Monitoring landslide displacement is therefore critical, as deformation patterns directly reveal both periodic variations and long-term deformation trends, serving as fundamental indicators for early warning and risk mitigation [4,5]. Accurate deformation prediction can support timely intervention to mitigate secondary disasters, thereby reducing casualties and economic losses. Traditional ground-based displacement measurements, such as leveling surveys and GNSS, are constrained by sparse sampling and high maintenance costs, limiting their scalability for regional monitoring where landslide events are numerous and spatially heterogeneous. With the rapid development of spaceborne remote sensing techniques, Interferometric Synthetic Aperture Radar (InSAR) has emerged as a powerful tool for landslide monitoring. Owing to its ability to provide all-weather, all-day, high-precision measurements of subtle ground deformation, InSAR enables large-scale and systematic monitoring. This capability effectively overcomes the limitations of traditional methods and substantially enhances the prediction and understanding of landslide kinematics [6,7,8].

Classical InSAR-based approaches for landslide displacement prediction have traditionally relied on statistical or physical models [9,10]. While such methods can capture fundamental deformation trends, they are often limited in modeling the complex and non-linear nature of slope instability. With the rapid advancement of artificial intelligence, machine learning and deep learning have given rise to data-driven models that excel in modeling complex temporal patterns, yielding substantial gains in prediction accuracy. Early machine learning studies demonstrated the potential of data-driven prediction. For instance, Zhou et al. [11] applied a Kernel-based Extreme Learning Machine (KELM) to decomposed trend and seasonal components for forecasting the Shuping landslide, while Shihabudheen and Peethambaran [12] integrated rainfall and reservoir water level (RWL) into an adaptive neuro-fuzzy inference system to model the Baijiabao landslide in the Three Gorges Reservoir Area (TGRA). Building on this direction, Han et al. [13] employed a hybrid Support Vector Machine (SVM) framework to account for external triggers influencing rapid landslide movement. Recognizing that InSAR-derived deformation time series are influenced by multiple exogenous factors, Ma and Mei [14] pointed out the challenge of capturing multi-variable interactions without significant information loss, emphasizing the need for more expressive models. Deep learning methods were subsequently introduced to overcome these limitations and to better capture non-linear patterns and long-term dynamics in displacement time series. Convolutional neural networks (CNNs) have been used to extract local characteristics [15], but their reliance on fixed-size receptive fields limits their ability to capture long-range dependencies, resulting in incomplete representations. Recurrent neural networks (RNNs), such as Gated Recurrent Units (GRUs), address sequential modeling by maintaining hidden states over time and have achieved improved accuracy in forecasting, such as in the Jiuxianping landslide case [16]. However, recurrent models may degrade in performance when handling long sequences.

To tackle these issues, attention-based deep neural networks have recently been introduced into InSAR time series analysis. Unlike CNNs and RNNs, attention mechanisms allow models to directly capture pairwise relationships between all time steps, regardless of distance, by allocating adaptive weights across features and temporal dimensions. This makes it possible to model both short-term fluctuations and long-term dependencies within a unified framework. For example, Zhang et al. [17] and Li et al. [18] integrated attention mechanisms with GRU and geographically weighted LSTM architectures to capture spatiotemporal patterns, which are crucial for analyzing land subsidence and slope instability. Rouet-Leduc et al. [19] combined attention with convolutional autoencoders to detect millimeter-scale deformations, and ref. [20] proposed a hybrid RNN-LSTM model to detect change points in InSAR-derived time series, enabling monitoring of seismic faults, subsidence, and landslides. More recently, Zhou et al. [21] integrated BiGRU with attention to better capture the underlying mechanisms of landslide deformation and anticipate triggered ground motions.

Beyond InSAR-specific architectures, recent progress has also highlighted the potential of deep learning for landslide displacement forecasting across spatial scales, with an increasing emphasis on operational relevance. Nava et al. [22] systematically benchmarked seven deep learning architectures across geographically diverse landslide sites, and their subsequent work [23] leveraged displacement residual analysis to detect regime shifts and calibrate early-warning thresholds. At broader scales, Dun et al. [24] developed scenario-based spatiotemporal deep learning frameworks for hillslope deformation prediction under varying environmental conditions in the Three Gorges Reservoir Area. He et al. [25] proposed a space–time hillslope deformation modelling framework combining graph-Transformer with temporal convolutional networks (TCNs), achieving promising prediction accuracy across extensive mountainous areas (∼15,000 km²). Despite these advances, most learning-based methods, particularly deep neural networks, usually suffer from limited interpretability due to their internal “black box” nature. This opacity impedes their widespread adoption in practical applications, where transparency and causal reasoning are essential for building trust and supporting decision-making [26,27]. Consequently, there is a pressing need for models that not only achieve high predictive accuracy but also provide interpretable, spatiotemporal feature attributions of how environmental inducing triggers and displacement kinematics interact to drive slope instability.

Motivated by this gap, we focus on interpretability analysis for multivariate forecasting in this study. We propose PatchTST-Fusion, a Transformer-based forecasting framework that achieves state-of-the-art predictive ability while providing transparent, temporally resolved attributions of environmental triggers to slope kinematics. The model extends the original PatchTST architecture [28] with a learnable channel fusion module, enabling principled modeling of both independent effects and synergistic interactions among displacement history, rainfall, and RWL fluctuation. To move beyond the “black-box” nature of deep learning, we further integrate interpretability analysis via TimeSHAP [29], which provides temporal and feature-level attributions across the input sequence. This hybrid design not only improves displacement forecasting accuracy but also provides transparent, spatiotemporal feature attribution that explain the mechanisms underlying slope instability, thereby aligning with the growing demand for explainable and actionable AI in geohazard monitoring. The main contributions of this study can be summarized as follows:

(i)

PatchTST-Fusion architecture: We propose a novel forecasting model that extends the PatchTST framework with a learnable channel fusion module, enabling principled modeling of both independent and synergistic effects among displacement history, rainfall, and reservoir water level fluctuations.

(ii)

Integration of interpretable deep learning: We incorporate TimeSHAP into the prediction pipeline, providing temporal and feature-level attributions that reveal how environmental triggers contribute to displacement kinematics.

(iii)

Enhanced forecasting performance: The proposed PatchTST-Fusion achieves enhanced accuracy in predicting future displacement compared to existing deep learning baselines.

2. Study Area and Data

2.1. Study Area

The Daping landslide cluster (hereafter also referred to as the Daping landslides) is located on the left bank of the Yangtze River in Badong County, Hubei Province, approximately 60–70 km upstream of the Three Gorges Reservoir (TGR), as shown in Figure 1. The cluster is composed of several reservoir landslides, including Hengliangzi, Daping, Chaiwan, and Songjiawuchang, distributed from east to west along the river. Gullies define the lateral boundaries between sublandslides, while the rear margin is marked by an amphitheater-like escarpment about 10 m high with an inclination of 40–50°. The landslide bodies range in thickness from 10 to 90 m. Internally, the slopes display a reverse configuration that produces a distinct topographic discontinuity.

Geologically, the strata exposed in the Daping landslide area belong to Members 1 to 4 ($T_2{b}^1$, $T_2{b}^2$, $T_2{b}^3$ and $T_2{b}^4$) of the Middle Triassic Badong Formation. The surficial material consists mainly of a layer approximately 10 m thick of purplish-red gravelly soil derived from $T_2{b}^2$, composed predominantly of mudstone and siltstone. Borehole investigations reveal that the landslide mass is relatively thin near the rear margin and thickens toward the central and frontal zones, reaching up to nearly 80 m, with an average thickness of approximately 40 m [30]. Beneath the gravelly soil, the body is underlain by highly fractured rock masses composed of purplish-red and grey mudstone and marl. The clasts are primarily derived from $T_2{b}^1$ and $T_2{b}^2$, and include purplish-red mudstone and siltstone as well as grey to yellowish-grey limestone and marl. The rock mass is pervasively fractured, locally occurring as large isolated blocks, and is generally classified as moderately to highly weathered.

2.2. SAR, RWL and Precipitation Data

The C-band Sentinel-1 satellite, launched by the European Space Agency in 2014, operates at a wavelength of 0.0555 m and provides single-look pixels with a resolution of approximately 13.9 m in the azimuth direction and 2.3 m in the range direction. In this study, we utilize ascending-track Path 11 data covering the Daping landslides. A total of 190 scenes, acquired between 2017 and 2022, were processed to construct the displacement time series for subsequent analysis. Daily RWL data from the TGR were collected, along with rainfall records from the Climate Hazards Group InfraRed Precipitation with Station (CHIRPS) dataset, which merges in situ and satellite observations into gridded precipitation data with ∼5 km (0.05°) spatial resolution [31].

3. Methodology

Figure 2 illustrates the overall workflow of the proposed framework for predicting landslide displacement from MT-InSAR data. The approach consists of four main steps:

(i)

InSAR Processing: Sentinel-1 SAR data covering the Daping landslides from 2017 to 2022 were processed using the Copernicus DEM (30 m, one arc-second resolution) for image co-registration and topographic phase removal.

(ii)

Time Series Denoising: The InSAR-derived displacement time series were interpolated and filtered to obtain both long-term and transient kinematics. Variational mode decomposition (VMD) was then applied to remove noise components and extract representative trend and seasonal modes.

(iii)

Prediction with deep learning: After denoising, displacement time series were combined with environmental triggers, i.e., rainfall and RWL fluctuations, for predictive modeling. To ensure regional representativeness, daily mean precipitation was computed within a 10 × 10 km window centered on the Daping landslides. To align with Sentinel-1’s 12-day revisit cycle, both precipitation and RWL data were resampled on SAR acquisition dates, thereby generating temporally consistent auxiliary inputs. These data were used as input sequences in the proposed PatchTST-Fusion model to predict future displacements.

(iv)

Accuracy Evaluation and Interpretable Deep Learning: Model performance was quantitatively evaluated to verify predictive reliability. In addition, TimeSHAP was incorporated into the pipeline, providing temporal and feature-wise attributions of displacement history, rainfall, and RWL fluctuations to the predicted displacement. This interpretability analysis offers transparent, interpretable insights into the environmental drivers of slope instability, thereby supporting robust early-warning and risk assessment.

Figure 2. The schematic diagram of the proposed framework, which contains InSAR processing, displacement time series denoising, prediction with the proposed PatchTST-Fusion, and feature attribution from environmental triggers using TimeSHAP. Below denotes the architecture of the proposed PatchTST-Fusion. Each input variable (displacement, rainfall, RWL) is treated as an independent univariate series, encoded by a shared PatchTST-based backbone. The latent representations are subsequently fused through a novel attention-based channel fusion module to capture both independent and synergistic effects.

Figure 2. The schematic diagram of the proposed framework, which contains InSAR processing, displacement time series denoising, prediction with the proposed PatchTST-Fusion, and feature attribution from environmental triggers using TimeSHAP. Below denotes the architecture of the proposed PatchTST-Fusion. Each input variable (displacement, rainfall, RWL) is treated as an independent univariate series, encoded by a shared PatchTST-based backbone. The latent representations are subsequently fused through a novel attention-based channel fusion module to capture both independent and synergistic effects.

The specific methodological components are described in detail in the following subsections.

3.1. Displacement Extraction via Multi-Temporal InSAR

MT-InSAR provides an effective means of monitoring slow ground deformation by exploiting time series of SAR acquisitions collected over long periods [8,21,32,33]. Its performance, however, is influenced by factors such as radar wavelength, satellite revisit interval, and terrain scattering properties. Among existing methods, the Small Baseline Subset (SBAS) technique has been widely adopted due to its ability to achieve both high monitoring accuracy and dense spatial coverage [34]. In this study, interferometric pairs were generated using the LiCSAR system [35], and displacement time series were estimated with the Stanford Method for Persistent Scatterers Multi-Temporal InSAR (StaMPS-MTI) [36]. In the SBAS implementation of StaMPS-MTI, candidate targets are selected based on the stability of their filtered interferometric phase, retaining those with minimal temporal incoherence. Specifically, pixels are preserved if their amplitude difference dispersion remains below a typical threshold of 0.6. The amplitude difference dispersion is defined as the standard deviation of amplitude differences between master and slave images, normalized by the mean amplitude. To ensure reliable retrievals, a three-dimensional phase unwrapping strategy was applied. Further details of the StaMPS-MTI method can be found in Hooper et al. [37,38], which have been validated and examined in numerous studies.

3.2. Displacement Time Series Denoising Using Variational Mode Decomposition

The observed landslide displacement time series can be conceptually decomposed into three components, i.e., a long-term trend, a periodic term, and stochastic noise. This can be expressed as

$$D_t=T_t+P_t+N_t$$

(1)

where $D_t$ denotes the observed total displacement at time t, $T_t$ represents the trend displacement, $P_t$ corresponds to the periodic displacement, and $N_t$ accounts for the residual noise. To enhance prediction accuracy, we employed VMD to adaptively decompose the displacement time series into a predefined number of intrinsic modes with distinct frequency characteristics [39]. The VMD principle can be formulated as a constrained variational optimization problem:

$$\begin{array}{cc}\hfill & \underset{u_k,{\omega }_k}{min}\left\{\sum _k{\left|{\partial }_t\left[\left(\delta \left(t\right)+{\displaystyle \frac{j}{\pi t}}\right)\ast u_k\left(t\right)\right]e^{-j{\omega }_{k}t}\right|}_2^2\right\}\hfill \\ \hfill & \mathrm{s}.\mathrm{t}.\sum _k{u}_k\left(t\right)=f\left(t\right)\hfill \end{array}$$

(2)

where $f\left(t\right)$ denotes the input displacement time series, $u_k\left(t\right)$ is the set of modal functions for the displacement time series at time t, $w_k$ represents the set of center frequencies, k is the total number of decomposed components, and $\delta$ is the Dirac distribution.

When applied to landslide displacement time series, VMD decomposes the original signal into a set of intrinsic mode functions (IMFs), each representing oscillatory behavior within a specific frequency band. These IMFs were subsequently reconstructed into three physically interpretable components: a long-term trend, a periodic or seasonal component, and a residual component. The trend component mainly reflects gravity-driven creep along the sliding surface, whereas the periodic component represents deformation responses associated with external triggers, such as rainfall and reservoir water level fluctuations. The residual component is primarily attributed to atmospheric artifacts, residual phase errors, measurement noise, and other unmodeled processes. In this study, the residual component was removed, and the reconstructed trend-plus-periodic signal was used as the denoised displacement series for subsequent forecasting. This decomposition allows the prediction task to move beyond direct data fitting toward a more process-aware representation of landslide kinematics.

3.3. PatchTST with Learnable Channel Fusion

Landslide deformation is a complex non-linear process driven by both internal material properties and external environmental triggers. To model these complex dependencies, we propose PatchTST-Fusion, a Transformer-based deep neural network designed to capture the temporal dynamics of displacement together with the influences of rainfall and RWL fluctuations. The framework, illustrated in Figure 2, leverages a channel-independent PatchTST backbone combined with a novel channel fusion module.

We denote the multivariate time series as

$$\mathbf{X}={[{\mathit{x}}_1,{\mathit{x}}_2,{\mathit{x}}_3]}^T$$

(3)

where ${\mathit{x}}_1$, ${\mathit{x}}_2$, and ${\mathit{x}}_3$ represent displacement, rainfall, and RWL fluctuations, respectively. At each time step t, the model considers a lookback window of length L, thereby encoding temporal dependencies from the past L observations. Each univariate series is divided into overlapping patches of length P with stride S, producing patch sequences ${\mathit{x}}_i^p\in {\mathbb{R}}^{P\times N}$, where $i\in 1,2,3$ indexes features and N is the number of patches. Each patch is projected into a D-dimensional latent space via a learnable projection $\mathbf{W}p\in {\mathbb{R}}^{D\times P}$, and augmented with positional embeddings $\mathbf{W}pos\in {\mathbb{R}}^{D\times N}$:

$${\mathit{x}}_d^{\left(i\right)}={\mathbf{W}}_p{\mathit{x}}_i^p+{\mathbf{W}}_{pos}$$

(4)

The embedded patches are then processed by the Transformer encoder. For each attention head $h\in 1,\dots ,H$, queries, keys, and values are computed as

$$\begin{array}{cc}\hfill {\mathbf{Q}}_h^{\left(i\right)}& ={\left({\mathit{x}}_d^{\left(i\right)}\right)}^T{\mathbf{W}}_h^Q\hfill \\ \hfill {\mathbf{K}}_h^{\left(i\right)}& ={\left({\mathit{x}}_d^{\left(i\right)}\right)}^T{\mathbf{W}}_h^K\hfill \\ \hfill {\mathbf{V}}_h^{\left(i\right)}& ={\left({\mathit{x}}_d^{\left(i\right)}\right)}^T{\mathbf{W}}_h^V\hfill \end{array}$$

(5)

with ${\mathbf{W}}_h^Q,{\mathbf{W}}_h^K\in {\mathbb{R}}^{D\times d_k}$ and ${\mathbf{W}}_h^V\in {\mathbb{R}}^{D\times D}$. The self-attention output is given by

$$\begin{array}{cc}\hfill {\left({\mathbf{O}}_h^{\left(i\right)}\right)}^T& =\mathrm{Attention}(Q_h^{\left(i\right)},K_h^{\left(i\right)},V_h^{\left(i\right)})\hfill \\ & =\mathrm{Softmax}\left({\displaystyle \frac{Q_h^{\left(i\right)}{K_h^{\left(i\right)}}^T}{\sqrt{d_k}}}\right)V_h^{\left(i\right)}\hfill \end{array}$$

(6)

Residual connections, feed-forward layers, and normalization are applied to obtain the final latent representation ${\mathit{z}}^{\left(i\right)}\in {\mathbb{R}}^{1\times D}$ for each channel.

To better capture the complex non-linear relationships between triggering factors and landslide kinematics, we propose a novel channel fusion module that integrates multi-head attention with dynamic pairwise interaction over PatchTST-encoded latent representations. Multi-head attention learns channel-specific weights

$$\begin{array}{cc}\hfill h_k^{\left(i\right)}& ={\left({\mathit{z}}^{\left(i\right)}\right)}^T{\mathbf{W}}_k^{\mathrm{att}}+b_k^{\mathrm{att}}\hfill \end{array}$$

(7)

$$\begin{array}{cc}\hfill {\alpha }_k^{\left(i\right)}& ={\displaystyle \frac{exp\left(h_k^{\left(i\right)}\right)}{{\sum }_{j=1}^{F}exp\left(h_k^{\left(j\right)}\right)}}\hfill \end{array}$$

(8)

and aggregates features as

$${\mathbf{h}}_k^{\mathrm{att}}=\sum {\alpha }_k^{\left(i\right)}{\mathit{z}}^{\left(i\right)}$$

(9)

To capture synergistic effects, we modeled pairwise feature interactions with dynamic weighting for each unique feature pair $(i,j)$

$$\begin{array}{cc}\hfill {\mathit{z}}_{ij}& =[{\mathit{z}}_i,{\mathit{z}}_j]\in {\mathbb{R}}^{1\times 2d}\hfill \\ \hfill h_{ij}& ={\left({\mathit{z}}_{ij}\right)}^T{\mathbf{W}}^{\mathrm{int}}+b_{ij}\hfill \\ \hfill {\beta }_{ij}& ={\displaystyle \frac{exp\left(h_{ij}\right)}{{\sum }_{k<l}exp\left(b_{kl}\right)}}\hfill \end{array}$$

(10)

The interaction representation is then computed as

$${\mathbf{h}}^{\mathrm{int}}=\sum _{i<j}{\beta }_{ij}({\mathbf{h}}_i\odot {\mathbf{h}}_j)$$

(11)

where ⊙ denotes an elementwise product. Finally, the outputs from attention-based fusion and interaction modeling are concatenated, flattened, and mapped to the displacement forecast ${\widehat{y}}_{t+1}$ through a linear regression head.

3.4. Feature Attribution from Triggers Using TimeSHAP

To provide interpretability for deep learning, we adopt TimeSHAP, a model-agnostic, post hoc framework for explaining sequence-based models [29]. TimeSHAP extends KernelSHAP by introducing temporal perturbations and pruning strategies [40], enabling attribution at the event (time step), feature, and feature-time cell levels. Given a sequential input of landslide displacement $\mathbf{X}$ and a trained predictive model f based on PatchTST-Fusion, TimeSHAP attributes an importance score to each feature-time cell $X_{i,t}$, quantifying its contribution to the model’s output $f\left(\mathbf{X}\right)$. The core principle is to approximate the local behavior of f by learning an additive surrogate model g via Shapley values, applied to coalitions of features and time steps. The explanation model takes the form:

$$g\left(\mathbf{c}\right)=w_0+{\displaystyle \sum _{i=1}^m}{w}_i{c}_i$$

(12)

where $\mathbf{c}$ is a coalition indicator vector for the presence or absence of features or events, $w_0$ is the base value, i.e., output for an uninformative input, and $w_i$ is the importance of each coalition element. By applying TimeSHAP, we quantify both the temporal influence and the feature-level influence with attribution matrices. In this study of reservoir landslides, the feature-level influence refers to precipitation, RWL fluctuations, and displacement history. Aggregating attribution matrices across the test set reveals global patterns of causal relevance, providing transparent explanations of how environmental triggers and displacement history interact to drive slope instability.

4. Results

4.1. Experimental Setup and Performance Metrics

To clarify the effective data volume, quality-control procedure, and evaluation strategy, the learning dataset was constructed from quality-controlled MT-InSAR displacement time series. During StaMPS-MTI SBAS processing, candidate scatterers were selected based on the stability of the filtered interferometric phase, and pixels with an amplitude difference dispersion lower than 0.6 were retained. After this screening, approximately 1000 valid scatterers for this specific landslide and 190 acquisition epochs from 2017 to 2022 were used for model development. The VMD-reconstructed displacement series, obtained by removing the residual noise component while retaining the trend and periodic components, was used as the learning target for all models. No additional ad hoc outlier removal, unwrap-failure correction, or separate coherence-based masking was applied during the prediction stage.

We then adopted a joint spatial-temporal hold-out strategy to assess generalization. Specifically, 75% of the scatterers were randomly assigned to the training/validation set, while the remaining 25% were withheld as an independent spatial test set. Within each spatial subset, the earliest 75% of observations were used for model development, and the latest 25% were reserved for temporal testing, allowing evaluation on both spatially unseen scatterers and temporally unseen observations. Within the training portion, 15% of samples were further used for validation, hyperparameter tuning, model selection, and early stopping. Instance normalization was applied independently to each sample to reduce dependence on dataset-specific global statistics and improve transferability.

The landslide displacement prediction performance was evaluated using three standard metrics:

$$\begin{array}{cc}\hfill & \mathrm{RMSE}=\sqrt{{\displaystyle \frac{1}{N}}\sum _{i=1}^N{(\widehat{y}i-y_i)}^2}\hfill \\ \hfill & \mathrm{MAE}={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N}|\widehat{y}i-y_i|\hfill \\ \hfill & R^2=1-{\displaystyle \frac{\sum {i=1}^N{(\widehat{y}i-y_i)}^2}{\sum {i=1}^N{(y_i-\overline{y})}^2}}\hfill \end{array}$$

(13)

where ${\widehat{y}}_i$, $y_i$, and $\overline{y}$ indicate the model prediction, the actual landslide displacement, and the mean value of the actual landslide displacement, respectively. RMSE and MAE are two of the most widely used metrics for continuous variables, reflecting the root mean squared error and the mean absolute deviation between predictions and observations, respectively. ${\mathrm{R}}^2$ represents the coefficient of determination, which quantifies the proportion of variance in the observed series explained by the model. Its value ranges from −1 to 1: $R^2=1$ indicates a perfect fit, $R^2=0$ implies performance equivalent to predicting the mean, and negative values indicate worse performance than a simple average-based prediction.

4.2. MT-InSAR Deformation and Configuration of Environmental Triggers

Figure 3a presents the InSAR-derived deformation map and spatial distribution of scatterers across the Daping landslide cluster. Pronounced deformation is concentrated in the west-central region, particularly at the junction of the western two sublandslides (i.e., the Songjiawuchang and Chaiwan landslides) and in the posterior section of the Songjiawuchang landslide. The maximum annual deformation rate reaches approximately $-53$ mm/yr. The histogram in Figure 3b summarizes the statistical distribution of scatterer velocities, revealing an average deformation rate of $-22.06$ mm/yr. Notably, $64.31\%$ of scatterers exhibit annual deformation rates between $-10$ and $-30$ mm/yr, while $26.76\%$ exceed $-30$ mm/yr. Only $8.93\%$ of scatterers show relatively mild deformation with rates slower than $-10$ mm/yr, indicating that large-scale instability dominates the landslide cluster.

Figure 3c compares the cumulative InSAR displacement with 12-day cumulative rainfall and 12-day average RWL fluctuations. The RWL exhibits a regular discharge-impoundment cycle, which strongly coincides with step-like increments in cumulative displacement. In other words, the cycle of RWL coincides with the characteristic behavior of reservoir landslides and is likely driven by variations in seepage pressure. Precipitation records reveal substantial interannual variability, with markedly higher precipitation during 2017 and 2021 relative to the other years. Similarly, the precipitation cycle coincides with with the InSAR-derived displacement in the long-term sequence as well. These observations underscore the combined influence of both reservoir regulation and rainfall on the kinematic evolution of the reservoir landslides.

4.3. Comparison and Prediction of Landslide Kinematics

Denoising of Displacement Time Series. In this study, the VMD method was applied to decompose the InSAR-derived displacement. By examining the signal in the frequency domain, VMD adaptively separates the complex signal into a finite set of harmonic signals. Through decomposition and subsequent reconstruction, the residual noise term was removed, while the long-term trend and periodic components were preserved, yielding a denoised cumulative displacement time series that is suitable for prediction. To illustrate the denoising effect, four representative scatterers P1–P4, shown in Figure 1, were selected within the Daping landslide cluster. The corresponding VMD results are presented in Figure 4, where the original displacement time series are effectively decomposed and denoised. After denoising, the complex displacement time series become more interpretable, thereby enabling more precise forecasting and clearer identification of the underlying kinematic patterns driving landslide deformation.

Baselines for comparison. To better evaluate the performance of the proposed PatchTST-Fusion, we chose several established methods, including a recent attention-based algorithm for landslide forecasting [21], a state-of-the-art transformer-based model for long sequence time series forecasting (Informer, Zhou et al. [41]), and the original PatchTST [28] as our baselines. All models were tested using the same experimental settings.

Performance evaluation. To evaluate predictive performance, we selected an exemplary scatterer (P4) that exhibited the most significant deformation within the Hengliangzi sublandslide, located in the eastern sector of the landslide cluster, downstream along the Yangtze River, and in close proximity to the TGR. The cumulative displacement predictions obtained by different models are compared in Figure 5. The results demonstrate that the proposed PatchTST-Fusion achieves substantially higher accuracy than the baseline methods. Figure 5e quantitatively compares the prediction accuracy of the four methods. The upper panel reports the absolute values of MAE, RMSE, and ${\mathrm{R}}^2$. The results indicate that CNN-BiGRU-Attention yields the largest errors, with both MAE and RMSE exceeding 0.8 mm, while the Informer achieves moderate accuracy with somewhat reduced errors. The original PatchTST exhibits further improvement, reducing MAE and RMSE by nearly half compared to CNN-BiGRU-Attention. The proposed PatchTST-Fusion achieves the lowest MAE (∼0.38 mm) and RMSE (∼0.45 mm), highlighting its superior predictive accuracy. In terms of explanatory power, all models achieve relatively high ${\mathrm{R}}^2$ scores (>0.9), but PatchTST-Fusion slightly outperforms the others, reaching close to unity, thereby demonstrating its ability to capture nearly all variance in the observed displacement. The lower panel presents percentage improvements in the evaluation metrics. As can be seen, the proposed PatchTST-Fusion achieves about 7–55% improvement in MAE and 10–52% improvement in RMSE, surpassing the other baseline methods.

To further evaluate the robustness of the proposed PatchTST-Fusion, additional experiments were performed under the same experimental setup but with artificially introduced perturbations. Specifically, Gaussian noise with zero mean and a standard deviation equal to 15% of the standard deviation of the original displacement time series was added to the displacement input. For each model, the perturbation experiment was repeated 20 times using independent Gaussian noise realizations, with random seeds from 1 to 20 to ensure reproducibility. In Figure 5, the solid predicted displacement curve represents the result obtained from the original unperturbed input, whereas the shaded area denotes the prediction envelope derived from the perturbed trials. At each testing epoch, the upper and lower bounds of the envelope were calculated as the maximum and minimum predictions across the 20 perturbation trials, respectively. The reported $Rang{e}_{max}$ and $Rang{e}_{min}$ indicate the maximum and minimum widths of this prediction envelope during the testing period.

The results in Figure 5 show that all tested algorithms are still able to capture the main deformation characteristics under noise perturbations, although their prediction stability varies. Among the baselines, CNN-BiGRU-Attention and Informer exhibit larger prediction envelopes, particularly during periods of rapid deformation, indicating weaker resilience to input instability. The original PatchTST improves stability due to its patch-based representation, but still shows noticeable perturbation-induced variability. In contrast, the proposed PatchTST-Fusion achieves the narrowest prediction envelope and the smallest prediction bias across the perturbation trials. This perturbation analysis highlights the robustness of PatchTST-Fusion under moderate input disturbances, which is important for real-world geohazard forecasting where InSAR time series and environmental measurements are inevitably affected by measurement errors, atmospheric artifacts, and interpolation uncertainties.

4.4. Lag Effects and Feature Attribution

Our study integrates attention weights derived from TimeSHAP to enhance the interpretability and transparency of deep learning predictions. To better capture periodic landslide kinematics, a longer input sequence corresponding to more than two years was adopted. As illustrated in Figure 6, attribution heat maps capture the evolving feature weights associated with landslide kinematics. The model input consists of rainfall, RWL, and historical displacement, where t denotes feature weights at the current time step, and $t-1$ through $t-n$ representing progressively earlier lags. The horizontal axis indicates the timestamp of the input sequence, while the vertical axis reflects the temporal lag relative to the prediction moment. The resulting weights quantify the relative contribution of each input and lag to predicting slope deformation. Larger weights signify greater influence of the corresponding timestamp and triggering factor on landslide behavior. For detailed analysis, we focus on scatterer P4 with significant motion, a point located within the Hengliangzi sublandslide and closest to the TGR within the Daping landslide cluster. This site exhibits displacement that is strongly modulated by both precipitation and RWL fluctuations, making it an ideal case for investigating how feature attributions capture the dynamic coupling between environmental triggers and slope response.

The temporal evolution of feature attribution highlights three characteristic phases, as defined from Zhou et al. [42]. Phase I (May–August) is marked by rapid motion induced by reservoir operation, during which elevated attention aligns with the rapid drawdown of RWL each year [42], identifying reservoir regulation as the dominant driver of instability. Conversely, Phase II (October–January) shows attenuated and fluctuating weights, reflecting slope stabilization under sustained impoundment and elevated reservoir levels after the annual rainy season. By contrast, Phase III (July–September) corresponds to the rainy season, where rainfall variability exerts a pronounced influence on deformation dynamics, as captured by localized peaks in attribution.

Overall, these patterns underscore the ability of the proposed framework to disentangle the temporally shifting dominance of rainfall and reservoir forcing in shaping landslide kinematics. The lag-by-time attribution maps provide further evidence of the asynchronous controls exerted by rainfall and reservoir fluctuations on slope kinematics. For rainfall, the influence is highly intermittent and primarily concentrated at short lags (approximately 1–3 steps), suggesting that rainfall-induced surface water infiltration and rapid pore pressure changes drive slope responses in a temporally localized manner. In contrast, reservoir regulation exhibits a more persistent and structured pattern, i.e., the strongest attributions appear consistently at the most recent lags ($t_1$–$t_2$) but extend intermittently to more distant lags ($t_4$–$t_6$), reflecting both immediate hydraulic loading and delayed seepage propagation within the slope mass.

To further unravel the dynamic contributions of rainfall and reservoir operations to landslide evolution, we computed Shapley values to quantify the relative importance of each trigger over the study period. Figure 7 shows the temporal variation in normalized Shapley values of rainfall and reservoir water level, juxtaposed with the observed deformation trajectory. This joint representation enables direct comparison between causal drivers and the modeled slope response. Figure 7a shows the temporal variation in normalized causal influences of the triggers compared with the observed deformation trajectory from a single sample point with the most significant displacement over the Hengliangzi sublandslide, namely P4. For this scatterer with significant deformation, the reservoir signal emerges as the dominant control, i.e., its SHAP values are consistently higher than those of rainfall, showing pronounced peaks that coincide with major shifts in the deformation trajectory. Rainfall contributions remain comparatively small, though transient surges are evident during certain intervals, indicating episodic triggering effects. The predicted deformation closely follows the observed displacement, underscoring the model’s ability to capture both the sustained reservoir influence and the intermittent rainfall modulation.

By contrast, results of Figure 7b derived from the entire landslide cluster reveal a pattern that differs from the single-point result, indicating a distinct temporal structure in external forcing across the entire landslide cluster. Reservoir operations exhibit a sustained and relatively smooth influence on slope deformation, with pronounced peaks coinciding with periods of drawdown and impoundment. In contrast, rainfall displays a more transient and fluctuating pattern, with sharp and short-lived peaks that align with the RWL curve. This suggests that rainfall primarily acts as a short-term trigger, amplifying slope response over limited intervals, whereas reservoir fluctuations impose a more stable and systematic control on slope kinematics. While both triggers contribute when considering the entire landslide area, their relative influences are roughly on the same order of magnitude.

In addition, across both individual samples and ensemble analyses, the results reveal a clear temporal lag between external triggers and slope kinematics. For the Daping landslides, the causal influence of reservoir fluctuations systematically precedes that of precipitation by approximately one to three prediction steps, i.e., 12–36 days. Importantly, this delay is not constant; rather, it varies across seasons and years, reflecting the evolving interaction between hydrological forcing and slope response. Such non-stationary lag behavior and magnitude can be captured through interpretable deep learning, which disentangles the time-dependent contributions of anthropogenic regulation and natural rainfall to landslide dynamics.

5. Discussion

5.1. Slope Instability and Geological Properties

The Daping landslide cluster is underlain by loose deposits from the 1st to 4th members of middle Triassic, consisting of silty clay interbedded with purplish-red gravelly soil that provides abundant material for slope instability. Preliminary investigations indicate that it is a reactivated historical failure that has remained largely stable over the long term, although localized deformation has occurred at the surface and along the leading edge of the landslide body, with notable deformations in 2013, 2014, and 2022 [30]. Previous studies have shown that the leading edge of the landslide is particularly prone to seepage-induced failures due to the poor permeability of the landslide body. Both rainfall and RWL fluctuations act as critical external triggers, with the mid-to-rear sections especially sensitive to rainfall. Increased precipitation elevates soil water content, reduces shear strength, and accelerates seepage through the sliding body. The resulting softening of slip-zone soils and elevated pore-water pressures further diminishes slope stability. During periods of intense rainfall, water rapidly infiltrates through the loose soil structure into the underlying aquiclude, where accumulation induces softening of the slip zone and promotes failure. Similarly, rapid drawdown of the reservoir generates a hydraulic head difference between groundwater within the slope and the external reservoir level. The outward seepage force associated with this imbalance increases the driving force of the landslide, thereby enhancing the possibility of instability.

5.2. Predicting Landslide Instability Using PatchTST-Fusion

The experimental results demonstrate that the proposed PatchTST-Fusion consistently outperforms baseline methods in forecasting landslide displacement. Compared to the effective CNN-BiGRU-Attention model proposed by Zhou et al. [21], which primarily captures local dependencies but struggles with long-range temporal relationships, PatchTST-Fusion leverages its patching mechanism to integrate both short-term fluctuations and long-term dependencies. This capability is particularly valuable in slow-moving landslide monitoring, where deformation occurs across heterogeneous timescales, i.e., rapid responses associated with rainfall-induced or reservoir-driven forcing factors often coexist with seasonal kinematics. By explicitly segmenting the long input sequence into patches, the model effectively disentangles these multi-scale dynamics, thereby enhancing predictive capability.

Moreover, the learnable channel fusion module facilitates joint reasoning across displacement history, precipitation, and RWL fluctuations. Unlike approaches that rely on simple concatenation or assume strict channel independence, the proposed attention-based fusion mechanism adaptively weights the contribution of each feature while simultaneously modeling synergistic interactions. This design aligns with the physical reality of slope instability, where landslides are rarely triggered by a single factor but instead arise from the coupling effects of multiple environmental drivers. Another important advantage of PatchTST-Fusion is its robustness, which is essential for real-world InSAR applications where atmospheric delays, orbital errors, and decorrelation often contaminate the measurements. Our robustness experiments indicate that the model maintains predictive stability even when subjected to moderate perturbations, highlighting its resilience and reliability in practical landslide monitoring.

Furthermore, by integrating TimeSHAP into the predictive pipeline, the framework helps address the “black-box” issue of conventional deep learning. The feature attribution from environmental triggers produced by TimeSHAP quantifies temporal and feature-wise contributions of rainfall, reservoir fluctuations, and displacement history, providing interpretable explanations that complement the numerical forecasts. Analysis of the Shapley values and feature heatmap derived by TimeSHAP reveals a physically meaningful partitioning of influences, i.e., heavy rainfall and rapid RWL regulation dominate short-term responses, promoting water infiltration and reducing the shear strength of the unstable slopes, eventually producing step-like displacement patterns, whereas long-term landslide evolution is mainly triggered by intrinsic rock and soil properties together with annual seasonal fluctuations from both triggers [3,43]. These insights are consistent with field-based observations of reservoir landslides. Beyond the immediate landslide case, the proposed framework has broader applicability to other geohazards involving ground surface deformation, such as subsidence from groundwater withdrawal and volcanic inflation. The hazard-specific triggers (e.g., groundwater levels, gas emissions, or soil moisture) can be seamlessly incorporated, thus paving the way for a unified, interpretability analysis platform for multivariate time series geohazard prediction.

5.3. Forecast Reliability and Operational Deployment

To assess the practical utility of the PatchTST-Fusion model for geohazard early warning, we extended the forecasting experiment from 1 to 5 time steps using an autoregressive prediction strategy, where each subsequent prediction uses the model’s own output from the previous step as input. This recursive approach covers horizons from approximately 12 to 60 days and represents a realistic operational scenario where future observations are unavailable. Figure 8a presents the horizon-dependent forecasting errors computed from held-out test samples.

While the displacement increment over a single 12-day interval may appear modest, the operational value of such forecasts should not be judged solely by one-step amplitude. Instead, hazard relevance is more appropriately interpreted through (i) cumulative deformation over decision-relevant windows, (ii) derived kinematic indicators such as velocity and acceleration, and (iii) threshold-based decision support for early warning.

A key observation from Figure 8a is that forecast errors accumulate approximately linearly with lead time despite the iterative prediction scheme. This is notable because autoregressive predictions are inherently susceptible to error propagation, where small errors can compound exponentially in unstable models. The observed linear growth indicates that PatchTST-Fusion captures the underlying deformation dynamics robustly without catastrophic error accumulation. Figure 8b visualizes this behavior for a representative held-out scatterer: predicted trajectories progressively diverge from the ground truth, yet maintain the overall deformation trend and seasonal patterns even at $h=5$.

The results demonstrate a robust operational capability across three complementary use cases:

(i)

Short-term nowcasting ($\mathit{h}=\mathbf{1}$): With an RMSE of 0.45 mm, the model enables early detection of subtle acceleration phases, supporting rolling-update monitoring as new Sentinel-1 acquisitions arrive.

(ii)

Cumulative trend warning ($\mathit{h}=\mathbf{2}–\mathbf{3}$): At the 36-day horizon, the accumulated RMSE remains below 4 mm after three iterative steps. For active reservoir landslides where displacement during this period can reach 60–90 mm, the prediction uncertainty remains small relative to the deformation signal, ensuring reliable flagging of hazardous trends.

(iii)

Strategic planning support ($\mathit{h}=\mathbf{4}–\mathbf{5}$): Even after five iterative steps (∼60 days), errors remain below 1 cm (RMSE ≈ 8.7 mm), providing valuable lead time for resource allocation. This stability under recursive prediction supports operational deployment where real-time observations are unavailable for intermediate steps.

Beyond point predictions, the framework supports scenario-driven forecasting when coupled with rainfall and reservoir water level outlooks. The TimeSHAP causal attribution further identifies which forcing factors dominate predicted acceleration, providing actionable guidance for targeted interventions, such as recommending extended drawdown periods when reservoir water level emerges as the primary driver.

In summary, the demonstrated stability of iterative multi-step predictions bridges the gap between high-precision monitoring and practical hazard mitigation, supporting a tiered operational workflow from daily nowcasting to monthly outlook products.

5.4. Distinguishable Triggering Effects via Deep Learning

Our study examined the six moments preceding each timestamp to evaluate how historical conditions shape current slope responses. The results clearly demonstrate that past fluctuations in triggering factors exert measurable impacts on present-day landslide displacement. This finding underscores that predicting slope kinematics is inherently a problem of complex temporal dynamics rather than simple regression. By leveraging the TimeSHAP module, the model effectively captures these lagged associations, offering deeper insights into the trigger interplay between external forcing and slope instability. Essentially, the framework distinguishes the lag effects of rainfall and reservoir fluctuations on the slope deformation, thereby disentangling their temporally offset contributions and magnitude in triggering the slope motion. It is not surprising that the representative point P4 is primarily influenced by reservoir operations, given its location within the westernmost sub-landslides of the Daping cluster and its close proximity to the TGR. Water level dominates the predictive attribution in this specific case study, suggesting it is the primary driver of the deformation variance. Throughout the observation period, reservoir regulation consistently exerted a stronger control on kinematic responses than precipitation. In contrast, when considering the entire landslide cluster, the contributions of reservoir fluctuations and rainfall were of comparable magnitude, though their impacts differed in timing.

These new findings can help us better understand the environmental triggering factors in prompting the landslide evolution in a more specific spatiotemporal domain over large regions. In contrast, achieving this capability with conventional geophysical modeling is challenging, as such methods typically require extensive field observations to capture environmental variability when estimating pore-water pressure and friction. This methodological advance is not limited to a single case, rather, the same strategy is in principle transferable to other landslides, subject to site-specific forcing and data quality, enabling deep learning models to reveal the evolving importance of environmental triggers across diverse settings, providing a more comprehensive and mechanistically informed perspective on the drivers of slope instability [44].

Our findings derived from interpretable deep learning provide a physically consistent interpretation of landslide-trigger interactions. Reservoir operations emerge as the dominant and persistent driver of slope evolution, imparting both immediate and sustained influences, while rainfall contributes episodic and short-lived amplifications of instability, i.e., rainfall effects are transient and episodic, whereas reservoir regulation exerts systematic and more stable control. This duality between anthropogenic regulation and natural forcing underscores the need to treat reservoir management not as background context but as an active, first-order control in fluvial-reservoir systems. Moreover, both the magnitude and timing of these lag effects fluctuate across the observation window, reflecting the non-stationary and evolving character of slope-trigger interactions. This dynamic lag structure, revealed only through interpretable deep learning, provides a mechanistic explanation for the variable delays observed between precipitation, reservoir level changes, and landslide deformation.

To further interpret this dynamic lag structure in a process-consistent manner, it is useful to view the slope response as a hydro-mechanical system governed by diffusion-like pore-pressure adjustment and drainage-dependent stress redistribution. In reservoir-controlled landslides, water level variations can be regarded as a boundary-condition forcing near the slope toe and submerged portions of the landslide body, which may induce both immediate hydraulic loading effects and delayed seepage adjustment within the slope mass. Such delayed responses are physically plausible because pore-pressure perturbations typically require time to propagate through the soil–rock matrix and to equilibrate under partially drained and seasonally varying conditions, thereby producing more persistent and structured lag signatures. By contrast, precipitation forcing is commonly mediated by infiltration and transient pore-pressure changes; its influence on displacement can be temporally localized when the effective pathway is shallow, or episodic when percolation intermittently connects to deeper shear zones depending on antecedent moisture. This process-based view is consistent with the attribution maps, where rainfall-related importance tends to concentrate at short lags, whereas RWL-related importance can extend to longer lags with a more sustained pattern.

Importantly, the inferred lag range (e.g., one to three prediction steps, corresponding to approximately 12–36 days under the Sentinel-1 revisit interval) should be interpreted as a site- and period-specific characterization rather than a universal constant. The apparent lag magnitude can vary with local hydrogeological and geomorphological properties, including permeability and stratigraphy, depth and connectivity of the active shear zone, drainage boundary conditions, seasonal hydrologic state, and antecedent moisture, all of which may evolve across years [45]. In addition, lag estimates are inherently constrained by the temporal sampling of InSAR observations, i.e., step-wise quantization at the acquisition interval. Therefore, while the attribution results provide useful evidence of asynchronous and non-stationary trigger–response timing for the Daping landslide cluster, transferring the same lag values to other sites or time periods without accounting for site-specific conditions should be done with caution.

5.5. Generalization and Transferability

The generalization capability of the proposed framework is evaluated through a combined spatial-temporal hold-out strategy, where 25% of scatterers over 25% of the time period are reserved for independent testing. This design ensures that test predictions are made for spatially unseen locations at temporally unseen time steps, demonstrating the model’s ability to generalize within the landslide cluster. The consistent performance across both training and testing subsets indicates that PatchTST-Fusion learns transferable representations of slope-trigger interactions rather than merely memorizing site-specific patterns.

For broader application beyond the current study area, we envision two complementary pathways. First, given the global coverage of Sentinel-1 data and the computational efficiency of our framework, training site-specific models for individual landslides is increasingly feasible. The architecture and hyperparameter configurations established here can serve as validated templates requiring only retraining on local data. Second, transfer learning offers promising avenues for rapid deployment to new sites with limited historical observations. The pre-trained PatchTST backbone could be fine-tuned on new sites, while the channel fusion module weights may transfer effectively between landslides sharing similar trigger mechanisms. The use of instance normalization further facilitates such transfer by ensuring that the model does not depend on dataset-specific normalization statistics. Systematic evaluation of cross-site transferability across landslides with varying dominant triggers represents an important direction for future research.

5.6. Physical Interpretation and Limitations

A primary concern in landslide displacement forecasting is the selection of input variables that adequately represent the slope’s stability mechanism. As noted in classical engineering geological principles, landslide kinematics are governed by a combination of internal predisposing factors and external triggering factors. While we fully acknowledge that internal geological parameters are fundamental to determining where a landslide is susceptible to failure, their role in short-term time-series forecasting requires a distinct methodological treatment. In our framework, we prioritize dynamic triggers while treating static geological factors as latently encoded variables. This is based on the premise that geological structure and material properties are quasi-static over the observation period; they do not provide the temporal variance necessary for a sequence-to-sequence model to predict immediate future changes. Instead, the physical influence of these static factors is implicitly recorded in the historical displacement sequence itself.

The historical trajectory of a landslide effectively serves as a phenomenological fingerprint of its geological context. For instance, a slope characterized by weak slip-zone soils will exhibit a specific trend of gravitational creep and a high sensitivity to rainfall, whereas a slope with higher shear strength or different permeability will exhibit a more muted or delayed response. By utilizing a sufficient history of displacement as a core input, the PatchTST-Fusion model learns the kinematic identity of the slope. The deep learning network effectively infers the complex, non-linear transfer function between the external triggers and the slope’s movement, thereby encoding the geotechnical properties (e.g., permeability, shear strength) into the model’s latent space. The decomposition strategy that we applied separates the raw displacement into trend and seasonal components, which correspond to distinct physical driving forces. The trend component captures the secular, gravity-driven creep controlled by the slope’s viscoplastic geological properties, while the seasonal component captures the elastic or plastic deformation responses to periodic external drivers like rainfall and reservoir regulation. By explicitly modeling these components separately, our framework respects the physical reality that static geology governs the long-term deformation trend, while dynamic hydrology governs short-term fluctuations. Thus, while the model does not explicitly input geological parameters, its architecture is designed to disentangle and learn the specific kinematic behaviors that those parameters dictate.

6. Conclusions

In this study, we proposed a novel forecasting framework, PatchTST-Fusion, for multivariate InSAR time series prediction, with landslide displacement forecasting in the Three Gorges Reservoir area as a representative case. By extending the original PatchTST architecture with a learnable channel fusion module, the framework effectively models both independent and synergistic effects among displacement history, rainfall, and reservoir water level. Furthermore, by integrating TimeSHAP into the predictive pipeline, we provided fine-grained temporal and feature-level attributions that disentangle how rainfall, reservoir fluctuations, and displacement history jointly influence future landslide displacement. This interpretable deep learning framework enhances its scientific value by uncovering mechanistic insights into slope instability. Experimental results show that PatchTST-Fusion achieves consistently higher predictive accuracy compared to baseline methods. The robustness analysis further confirms that the model maintains stable performance in the presence of moderate noise, underscoring its reliability under real-world monitoring conditions where InSAR observations are often affected by atmospheric delays and decorrelation effects. Taken together, these findings indicate the potential of PatchTST-Fusion as an accurate, interpretable, and robust framework for InSAR time series forecasting. This work focuses on reservoir landslides with creeping, step-like motion features. As such, the model captures non-linear cumulative deformation well, but its performance on instantaneous failure modes, such as rock avalanches or brittle fracturing, remains an open question. Expanding the test cases to include these distinct kinematic regimes is a necessary next step to ensure the model’s transferability to different geological contexts. In future work, the methodology can be generalized to a wide range of ground surface deformation hazards, including seismic activity, subsidence, and volcanic activity, thereby providing a valuable tool for both scientific investigation and practical early warning.