## 1 Introduction  
Landslide deformation prediction is crucial in landslide monitoring and early warning. An accurate and effective deformation prediction model provides a scientific basis for early warnings, enabling rapid and timely alerts before abrupt landslide failures, thereby minimizing disaster-induced losses [1, 2]. Existing landslide forecasting models can be broadly categorized into empirical, statistical, and nonlinear theoretical [3]. Empirical models primarily rely on landslide formation mechanisms and long-term observational data for predictions and include the Saito [4] and Voight [5] models, which typically analyze the mathematical relationship between landslide velocity and the critical failure time. These models can effectively reflect the overall evolution trend in landslides; however, their predictive accuracy and applicability are constrained by their inability to account for the influence of external environmental factors such as rainfall. Statistical models use long-term observational data to predict landslide deformation, including the autoregressive integrated moving average [6; 7; 8] and the traditional GM (1, 1) [9; 10; 11] models. While these models effectively capture the historical evolutionary trends in landslide deformation, their predictive capability is limited by a lack of in-depth landslide physical mechanism modelling. Consequently, they struggle to accurately describe the dynamic influence of external environmental factors (e.g., rainfall and reservoir water levels) on the deformation process. With the rapid advancements in computer science and technology, nonlinear theoretical models have gained widespread applications in landslide prediction [12]. Machine learning models, owing to their strong data-driven capabilities and nonlinear mapping properties, can integrate multiple influencing factors such as rainfall and reservoir water levels. This overcomes the limitations of traditional empirical and statistical models in analyzing external factors, significantly enhancing the predictive performance of landslide deformation models [13; 14; 15; 16; 17; 18; 19; 20; 21]. Commonly used machine learning models include support vector machines [22; 23], long short-term memory (LSTM) networks [24; 25; 26], and deep neural networks [27]. Moreover, researchers have proposed various improvements to machine learning models, such as optimizing hyperparameters using intelligent optimization algorithms or employing ensemble learning and hybrid modeling techniques to combine different machine learning models, thereby improving prediction accuracy and generalization performance [28; 29; 30]. Examples include the Genetic Algorithm (GA)-optimized Elman neural network [31], the least squares support vector machine (LSSVM) prediction method based on the particle swarm optimization (PSO) algorithm [32], and wavelet denoising (WD)-(GA)-LSSVM [33]. However, these studies primarily focus on the temporal characteristics of long-term landslide evolution without considering the inherent spatial correlations in the landslide sliding process. Landslide deformation exhibits complex spatial correlations. Before experiencing overall instability and failure, a landslide typically undergoes a prolonged deformation evolution process [34]. Based on landslide dynamics and the initial failure location, landslides can be classified into four types: traction, thrust, translational, and composite landslides [35; 36; 37]. Thrust landslides are primarily driven by the development of tensile cracks in the upper slope, which induce the instability and initial sliding of the upper portion, subsequently pushing the lower section into motion. Translational landslides typically occur along relatively gentle sliding surfaces, where initial failure points are distributed across multiple locations on the sliding plane. These points slip simultaneously and gradually merge as deformation progresses.