## 1 Introduction  
Landslides, as one of the most widespread and frequent natural hazards all over the world, not only directly threaten human life but also cause tremendous damage to the human living environment, resources, and property. To minimize the losses caused by landslide hazards, many scholars have carried out research on landslide prediction [1; 2; 3; 4; 5]. Among them, landslide displacement forecasting has been a contentious issue [6; 7; 8; 9].  
At present, one of the most widely used ideas for landslide displacement forecasting is to decompose the original landslide displacement, and then forecast each subsequence separately, and finally reconstruct all forecast values to obtain the forecast results. Following this idea, in [10], wavelet analysis is used to decompose the landslide displacement and a particle swarm-optimized support vector machine is used as the forecasting model. In [11], empirical mode decomposition (EMD) is matched with an extreme learning adaptive neuro-fuzzy inference system for landslide displacement forecasting. In [12], ensemble empirical mode decomposition (EEMD) is adopted to analyze the landslide displacement, which avoids the mode aliasing problem in EMD. Similarly, the authors of [13] also used the EEMD technique to decompose rainfall, reservoir level, and landslide cumulative displacement sequences into residual sequence and finite intrinsic mode functions with frequencies ranging from high to low. Moreover, the forecasting model combined with intelligent algorithms, such as genetic algorithm-least squares support vector machine [14], genetic algorithm-back propagation neural network [15], and particle swarm-optimized support vector machine [16], is favored by researchers.  
Some achievements have been made in the above studies; however, there are some shortcomings in displacement analysis and forecasting models. For displacement analysis, wavelet analysis has some difficulties in determining the basis function and estimating the wavelet order; EMD and EEMD are random and uncontrollable for the decomposition number of landslide displacement, while excessive decomposition will increase the forecasting workload. For forecasting models, neural networks have a certain dependence on the size of data samples, and the selection of the support vector machine parameters has certain blindness due to manual setting, while intelligent algorithms can easily fall into a local optimum. Therefore, how to more scientifically and reasonably analyze the original time series and establish a high-performance forecasting model are the difficulties of landslide displacement forecasting research.  
To improve the forecast accuracy of landslide displacement, a dynamic forecasting model based on variational mode decomposition (VMD) and a stack long short-term memory network (SLSTM) is proposed. The main contributions of this paper are as follows:  
(1) VMD with strict mathematical theory and controllable decomposition number is applied to displacement analysis, which obtains stable and fixed displacement subsequences;  
(2) A SLSTM network with \"3 + 1\" layers is designed to model and forecast each displacement subsequence, which improves the performance of a basic long short-term memory (LSTM) network;  
(3) A dynamic forecasting method is proposed, which realizes long-term landslide displacement forecasting.  
The rest of this paper is organized as follows: Section 2 describes the basic principle and training method of the SLSTM network. Section 3 is devoted to describing the combined process of the VMD and the SLSTM network. The dynamic forecasting process based on the VMD-SLSTM network is also presented in this section. In Section 4, a real application case is introduced to verify the proposed forecasting model. Several comparative experiments are carried out to demonstrate the superiority of the proposed forecasting model. The last section draws conclusions.